MA026 Advanced Combinatorics

Faculty of Informatics
Spring 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
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).
The course is also listed under the following terms Spring 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/spring2025/MA026