CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Graph theory and combinatorics

Code Completion Credits Range Language
NI-GAK Z,ZK 5 2P+2C Czech
Garant předmětu:
Tomáš Valla
Lecturer:
Tomáš Valla
Tutor:
Michal Opler, Tomáš Valla
Supervisor:
Department of Theoretical Computer Science
Synopsis:

The goal of the class is to introduce the most important topics in graph theory, combinatorics, combinatorial structures, discrete models and algorithms. The emphasis will be not only on undestanding the basic principles but also on applications in problem solving and algorithm design. The topics include: generating functions, selected topics from graph and hypergraph coloring, Ramsey theory, introduction to probabilistic method, properties of various special classes of graphs and combinatorial structures. The theory will be also applied in the fields of combinatorics on words, formal languages and bioinformatics.

Requirements:

We expect knowledge of topics from the courses Algorithms and graphs I. and II. (BI-AG1, BI-AG2).

Syllabus of lectures:

List of the topics

1. Generating functions

2. Graph coloring and perfect graphs

3. Introduction to Ramsey theory

4. Matching in general graphs

5. Counting spanning trees

6. Introduction to probabilistic method

7. Extremal combinatorics

8. Planar graphs and Kuratowski theorem

9. Coloring graphs on surfaces

10. List coloring and choosability

11. Edge coloring

12. Combinatorial games

Syllabus of tutorials:

1. Generating functions

2. Graph coloring and perfect graphs

3. Introduction to Ramsey theory

4. Matching in general graphs

5. Counting spanning trees

6. Introduction to probabilistic method

7. Extremal combinatorics

8. Planar graphs and Kuratowski theorem

9. Coloring graphs on surfaces

10. List coloring and choosability

11. Edge coloring

12. Combinatorial games

Study Objective:
Study materials:

1. Bollobas, B. : Modern Graph Theory. Springer, 1998. ISBN 0-387-98488-7.

2. Graham, R. L. - Knuth, D. - Patashnik, O. : Concrete Mathematics. Addison-Wesley, 1994. ISBN 978-0-201-55802-9.

Note:
Further information:
https://courses.fit.cvut.cz/NI-GAK/
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomTH:A-942Valla T.11:00–12:30(lecture parallel1)Thákurova 7 (budova FSv)roomTH:A-942Opler M.Valla T.12:45–14:15(lecture parallel1parallel nr.101)Thákurova 7 (budova FSv)
The course is a part of the following study plans:
Data valid to 2024-05-27
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6120006.html