Graph theory and combinatorics

Course guarantor:

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. B. Bollobas : 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.

3. Diestel, R. : Graph Theory. Springer, 2016. ISBN 978-3-662-53621-6.

Note:

Further information:

https://courses.fit.cvut.cz/NIE-GAK/

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Master specialization Software Engineering, in English, 2021 (elective course)
• Master specialization Computer Security, in English, 2021 (elective course)
• Master specialization Computer Systems and Networks, in English, 2021 (elective course)
• Master specialization Design and Programming of Embedded Systems, in English, 2021 (elective course)
• Master specialization Computer Science, in English, 2021 (PS)
• Master specialization Computer Science, in English, 2024 (PS)