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Graph Theory I

Type of study Doctoral
Language of instruction Czech
Code 470-6302/01
Abbreviation TGI
Course title Graph Theory I
Credits 10
Coordinating department Department of Applied Mathematics
Course coordinator doc. Mgr. Petr Kovář, Ph.D.

Subject syllabus

Lectures
1) Graphs, simple graphs. Subgraphs. Degree, Incidence matrix and adjacency matrix
2) Paths and cycles. Distance and eccentricity.
3) Trees, spanning trees, bipartite graphs.
4) Graph isomorphisms, automorphisms.
5) Connectivity, cuts, bridges, blocks, articulations.
6) Matching and covers in graphs and bipartite graphs, assignment problem, perfect matching.
7) Edge coloring and its applications. Chromatic index. Vizing theorem.
8) Vertex coloring and its applications. Chromatic number. Brooks theorem.
9) Planar graphs and their applications. Euler formula. Kuratowski hteorem, Four color theorem.
10) Nonplanar graph, nonplanarity measures
11) Eulerian and a hamiltonian graphs.
12) Oriented graphs. Oriented paths, cycles and tournaments.
13) Flows in a network, cuts. Maximum flow and minimum cut theorem.
During the semester each student prepares one or two projects.

Literature

D. B. West, Introduction to graph theory - 2nd ed., Prentice-Hall, Upper Saddle River NJ, (2019), ISBN 9780131437371 .

Advised literature

Bondy, U.S.R. Murty: Graph Theory with Applications, American Esevier Publishing Co., New York, 1976, ISBN 0-444-19451-7 .
Behzad, G. Chartrand, L. Lesniak-Foster: Graphs and Digraphs, Prindle, Weber and Schmid, Boston, 197, ISBN 0-87150-261-5 .