MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2014
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Thu 9:00–11:50 G191m
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2012
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Tue 13:00–15:50 G191m
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2014.

MA051 Advanced Graph Theory I

Faculty of Informatics
Spring 2010
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Thu 9:00–11:50 B411
Prerequisites
Teorie grafu MA010 (Graph theory). Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTT.html
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory I

Faculty of Informatics
Spring 2008
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Wed 9:00–11:50 B411
Prerequisites
Teorie grafu MA010 (Graph theory). Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
Planar graphs, and more generaly graphs drawn on surfaces, play a (somehow surprisingly) important role in graph theory and in its applications. (For instance, the Four Colour theorem, the Graph Minor project, or various new efficient parametrized algorithms for hard graph problems.)
This subject introduces a mathematician or a theoretical computer scientist into the beauties of this branch of graph theory, often called topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
  • NEŠETŘIL, Jaroslav and Jiří MATOUŠEK. Invitation to discrete mathematics. Oxford: Clarendon Press, 1998, xv, 410 s. ISBN 0-19-850207-9. info
Assessment methods (in Czech)
This is an advanced course, taught in English, and conducted quite informally (seminar-type). Evaluation by a written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTT.html
The course is also listed under the following terms Spring 2006, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced topics in Graph Theory: Graphs on surfaces

Faculty of Informatics
Spring 2006
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Thu 14:00–15:50 B411 and each even Thursday 16:00–17:50 B411
Prerequisites
Usual basic knowledge of discrete mathematics and graphs. (See the book "Invitation to discrete mathematics".) Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 50 student(s).
Current registration and enrolment status: enrolled: 0/50, only registered: 0/50, only registered with preference (fields directly associated with the programme): 0/50
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
Planar graphs, and more generaly graphs drawn on surfaces, play a (somehow surprisingly) important role in graph theory and in its applications. (For instance, the Four Colour theorem, the Graph Minor project, or various new efficient parametrized algorithms for hard graph problems.)
This subject introduces a mathematician or a theoretical computer scientist into the beauties of this branch of graph theory, often called topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • (A graph view of surface classification.)
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
  • NEŠETŘIL, Jaroslav and Jiří MATOUŠEK. Invitation to discrete mathematics. Oxford: Clarendon Press, 1998, xv, 410 s. ISBN 0-19-850207-9. info
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. Vyd. 2., opr. Praha: Karolinum, 2000, 377 s. ISBN 8024600846. info
Assessment methods (in Czech)
Written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Further Comments
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTT.html
The course is also listed under the following terms Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2019

The course is not taught in Spring 2019

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Course is no more offered.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2018

The course is not taught in Spring 2018

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Course is no more offered.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2017

The course is not taught in Spring 2017

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Course is no more offered.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2016

The course is not taught in Spring 2016

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Course is no more offered.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2015

The course is not taught in Spring 2015

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2013

The course is not taught in Spring 2013

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Graph Theory MA010. Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory I

Faculty of Informatics
Spring 2011

The course is not taught in Spring 2011

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Prerequisites
Teorie grafu MA010 (Graph theory). Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTT.html
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory I

Faculty of Informatics
Spring 2009

The course is not taught in Spring 2009

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Prerequisites
Teorie grafu MA010 (Graph theory). Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
Planar graphs, and more generaly graphs drawn on surfaces, play a (somehow surprisingly) important role in graph theory and in its applications. (For instance, the Four Colour theorem, the Graph Minor project, or various new efficient parametrized algorithms for hard graph problems.)
This subject introduces a mathematician or a theoretical computer scientist into the beauties of this branch of graph theory, often called topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Assessment methods (in Czech)
This is an advanced course, taught in English, and conducted quite informally (seminar-type). Evaluation by a written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTT.html
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.

MA051 Advanced Graph Theory I

Faculty of Informatics
Spring 2007

The course is not taught in Spring 2007

Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Prerequisites
Usual basic knowledge of discrete mathematics and graphs. (See the book "Invitation to discrete mathematics".) Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 8 fields of study the course is directly associated with, display
Course objectives
Planar graphs, and more generaly graphs drawn on surfaces, play a (somehow surprisingly) important role in graph theory and in its applications. (For instance, the Four Colour theorem, the Graph Minor project, or various new efficient parametrized algorithms for hard graph problems.)
This subject introduces a mathematician or a theoretical computer scientist into the beauties of this branch of graph theory, often called topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • (A graph view of surface classification.)
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
  • NEŠETŘIL, Jaroslav and Jiří MATOUŠEK. Invitation to discrete mathematics. Oxford: Clarendon Press, 1998, xv, 410 s. ISBN 0-19-850207-9. info
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. Vyd. 2., opr. Praha: Karolinum, 2000, 377 s. ISBN 8024600846. info
Assessment methods (in Czech)
Written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further Comments
The course is taught once in two years.
The course is taught: every week.
Teacher's information
http://www.fi.muni.cz/~hlineny/Vyuka/
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014.
  • Enrolment Statistics (recent)