FI:MA026 Advanced Combinatorics - Course Information
MA026 Advanced Combinatorics
Faculty of InformaticsSpring 2025
- Extent and Intensity
- 2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching - Teacher(s)
- prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Mgr. Jan Grebík, Ph.D. (lecturer) - Guaranteed by
- prof. RNDr. Petr Hliněný, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics - Prerequisites
- MA010 Graph Theory
The subject *strictly requires* solid theoretical background in combinatorics, at least on the level of MA010 or equivalent courses. - 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 25 student(s).
Current registration and enrolment status: enrolled: 0/25, only registered: 0/25, only registered with preference (fields directly associated with the programme): 0/25 - fields of study / plans the course is directly associated with
- there are 33 fields of study the course is directly associated with, display
- Course objectives
- The goal is to introduce students into selected advanced areas of combinatorics, also refering to combinatorial algorithms and computational complexity of the studied problems.
- Learning outcomes
- After finishing the course, the students will understand selected advanced principles of combinatorics and graph theory; will be able to conduct research work in areas of combinatorics.
- Syllabus
- Advanced structural graph theory: graph minors and well-quasi-ordering, width parameters, matching in general graphs, list coloring, intersection graphs
- Topological graph theory: planarity testing and SPQR trees, MAXCUT algorithm in planar graphs, graphs on surfaces of higher genus, crossing numbers
- Probabilistic method: review of tools - linearity of expectation and concentration bounds, lower bounds on Ramsey number, crossing number, and list chromatic number, Lovász Local Lemma
- Regularity method: regularity decompositions, removal lemma, property testing algorithms
- Extremal Combinatorics: Hales-Jewett Theorem, Van der Waerden Theorem, Gallai-Witt Theorem
- Literature
- recommended literature
- DIESTEL, Reinhard. Graph theory. 4th ed. Heidelberg: Springer, 2010, xviii, 436. ISBN 9783642142789. info
- ALON, Noga and Joel H. SPENCER. The probabilistic method. 3rd ed. Hoboken, N.J.: Wiley, 2008, xv, 352. ISBN 9780470170205. info
- MOHAR, Bojan and Carsten THOMASSEN. Graphs on surfaces. Baltimore: The Johns Hopkins University Press, 2001, xi, 291. ISBN 0801866898. info
- Teaching methods
- Weekly lectures, bi-weekly tutorials, individual homework essays
- Assessment methods
- Individual homework essay 30%, oral exam 70%
- Language of instruction
- English
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week. - Teacher's information
- This subject will be taught at least once in two years. However, due to its highly specialized nature, it may not be taught every year if there are not sufficiently many registered students (say, more than 5).
- Enrolment Statistics (Spring 2025, recent)
- Permalink: https://is.muni.cz/course/fi/spring2025/MA026