MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory I
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory I
Faculty of InformaticsSpring 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
- 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
MA051 Advanced topics in Graph Theory: Graphs on surfaces
Faculty of InformaticsSpring 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory: Topological
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory I
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory I
Faculty of InformaticsSpring 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
- 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
MA051 Advanced Graph Theory I
Faculty of InformaticsSpring 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/
- Enrolment Statistics (recent)