Graph Theory

In order to register for the course 01PTG, the student must have successfully completed the course 01TG.

Garant předmětu:

Petr Ambrož

Lecturer:

Petr Ambrož, Jan Volec

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

1. Basic notion of graph theory.

2. Edge and vertex connectivity (Menger Theorem).

3. Bipartite graphs.

4. Trees and forests.

5. Spanning trees (Matrix-Tree Theorem).

6. Euler tours and Hamilton cycles.

7. Maximal and perfect matching.

8. Edge coloring.

9. Flows in networks.

10. Vertex coloring.

11. Plannar graphs (Kuratowski theorem), vertex coloring of planar graphs.

12. Spectrum of the adjacency matrix.

13. Extremal graph theory.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] R. Diestel: Graph Theory (5th ed.), Springer-Verlag Berlin Heidelberg 2017.

[2] M. Rigo: Advanced Graph Theory and Combinatorics, Wiley-ISTE 2016.

Optional references:

[3] A. Bondy, U.S.R. Murty: Graph Theory, Springer-Verlag London 2008.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (compulsory course in the program)
• Aplikované matematicko-stochastické metody (elective course)
• Aplikace informatiky v přírodních vědách (compulsory course in the program)
• Matematická fyzika (elective course)
• Matematické inženýrství (compulsory course in the program)
• Matematická informatika (compulsory course in the program)
• Fyzikální elektronika - Počítačová fyzika (elective course)
• Kvantové technologie (elective course)