MA052 Advanced Graph Theory: Structural

Faculty of Informatics
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: 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
Fri 8:00–10:50 G191m
Prerequisites
Graph theory MA010. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011.

MA052 Advanced Graph Theory II

Faculty of Informatics
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: 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 G124
Prerequisites
Graph theory MA010. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width or rank-width.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • MS2- and MS1-theorems.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more), 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://is.muni.cz/el/1433/jaro2011/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2013.

MA052 Advanced Graph Theory II

Faculty of Informatics
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)
RNDr. Robert Ganian, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Thu 14:00–16:50 B411
Prerequisites
Graph theory MA010. Some knowledge of algorithmic complexity and of predicate logic is 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
Structural graph theory is gaining more and more attention these days, mainly in connection with the Graph Minor Theory of Robertson and Seymour (which is one of the deepest results of discrete mathematics of all times). For instance, the theory implies existence of polynomial algorithms for many graph problems, sometimes even when it is not clear whether a problem is solvable at all. The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width.
In the course student shall learn about some cutting-edge recent development in graph theory.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minor Theorem, an outline.
  • Advanced width measures: clique-width, rank-width.
  • MS2- and MS1-theorems.
Literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
Assessment methods
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.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTS.html
The course is also listed under the following terms Spring 2007, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory II

Faculty of Informatics
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.
Timetable
Wed 9:00–11:50 B411
Prerequisites
Usual basic knowledge of discrete mathematics and graphs. (See the book "Invitation to discrete mathematics".) Some knowledge of algorithmic complexity.
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
Structural graph theory is gaining more and more attention these days, mainly in connection with the Graph Minor Theory of Robertson and Seymour (which is one of the deepest results of discrete mathematics of all times). For instance, the theory implies existence of polynomial algorithms for many graph problems, sometimes even when it is not clear whether a problem is solvable at all.
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minor Theorem, an outline.
  • Advanced width measures: clique-width, rank-width.
  • MS2- and MS1-theorems.
  • Extensions to structural matroid theory.
Literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
Assessment methods (in Czech)
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.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTS.html
The course is also listed under the following terms Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

Faculty of Informatics
Spring 2014

The course is not taught in 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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, such as tree-width or tree-depth or rank-width, and to graph minors.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications (metatheorems).
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • Sparse graph classes and depth measures.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • NEŠETŘIL, Jaroslav and Patrice OSSONA DE MENDEZ. Sparsity : graphs, structures, and Algorithms. Heidelberg: Springer, 2012, xxiii, 457. ISBN 9783642278747. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more) or tutorial presentation, 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://is.muni.cz/el/1433/jaro2013/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory: Structural

Faculty of Informatics
Spring 2012

The course is not taught in 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: 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. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width or rank-width.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • MS2- and MS1-theorems.
Literature
    required literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
    recommended literature
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. 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, or more), 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://is.muni.cz/el/1433/jaro2011/MA052/index.qwarp
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory II

Faculty of Informatics
Spring 2010

The course is not taught in 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.
Prerequisites
Graph theory MA010. Some knowledge of algorithmic complexity and of predicate logic is 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
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width or rank-width.
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 structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minors Theorem, an outline.
  • Advanced width measures: clique-width, rank-width, directed measures.
  • MS2- and MS1-theorems.
Literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. 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/Teaching/AGTS.html
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced Graph Theory II

Faculty of Informatics
Spring 2008

The course is not taught in 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.
Prerequisites
Usual basic knowledge of discrete mathematics and graphs. (See the book "Invitation to discrete mathematics".) Some knowledge of algorithmic complexity.
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
Structural graph theory is gaining more and more attention these days, mainly in connection with the Graph Minor Theory of Robertson and Seymour (which is one of the deepest results of discrete mathematics of all times). For instance, the theory implies existence of polynomial algorithms for many graph problems, sometimes even when it is not clear whether a problem is solvable at all.
The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width.
Syllabus
  • Repetition of basic graph terms.
  • Connectivity on graphs, different measures. Menger's theorem. Linking, submodular functions.
  • Width decompositions and measures: tree-width, branch-width. Algorithmic applications.
  • Minors and their basic properties, well-quasi-ordering, WQO on trees.
  • Planar graphs, drawing on surfaces, forbidden minors.
  • The Graph Minor Theorem, an outline.
  • Advanced width measures: clique-width, rank-width.
  • MS2- and MS1-theorems.
  • Extensions to structural matroid theory.
Literature
  • DIESTEL, Reinhard. Graph theory. New York: Springer, 1998, xiv, 286. ISBN 0387982108. info
Assessment methods (in Czech)
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/AGTS.html
The course is also listed under the following terms Spring 2007, Spring 2009, Spring 2011, Spring 2013.

MA052 Advanced topics in Graph Theory: Minors, Width, and Structural properties

Faculty of Informatics
Spring 2006

The course is not taught in 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.
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
Language of instruction
Czech
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 2007, Spring 2009, Spring 2011, Spring 2013.
  • Enrolment Statistics (recent)