Skip to main content
Skip header

Graph Theory

Type of study Follow-up Master
Language of instruction Czech
Code 470-4302/01
Abbreviation TG
Course title Graph Theory
Credits 6
Coordinating department Department of Applied Mathematics
Course coordinator doc. Mgr. Petr Kovář, Ph.D.

Subject syllabus

Lectures and discussions
- Graphs, simple graphs. Incidence matrix and adjacency matrix. Subgraphs. Degree of a vertex.
- Paths and cycles.
- Trees, bridges and cuts.
- Graph isomorphisms.
- Connectivity and blocks. Cut sets.
- Matching and covers in general and bipartite graphs. Perfect matchings.
- Edge colorings. Chromatic index, Vizing's Theorem.
- Vertex colorings, Chromatic number, Brook's Theorem.
- Planar graphs. Dual graphs, Euler's formula for connected planar graphs, Kuratowski's Theorem. Four Color Theorem.
- Non-planar graph, measures of non-planarity.
- Eulerian and Hamiltonian graphs.
- Oriented graphs. Oriented paths and cycles.
- Tournaments and graph models

Literature

J. Matoušek, J. Nešetřil, Chapters in Discrete Mathematics, Karolinum Praha (2010).

Advised literature

D. B. West, Introduction to graph theory, Prentice-Hall, Upper Saddle River NJ, (2019), ISBN 9780131437371 .