Introduction to Graph Theory A

Lecturer:

Petr Ambrož (gar.)

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course provides a coherent explanation of modern graph theory, some applications are discussed.

Requirements:

Syllabus of lectures:

1) Basic notion of graph theory

2) Edge and vertex connectivity (Menger Theorem)

3) Bipartite graphs

4) Trees and forests, cutting edges

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)

12) Spectrum of an adjacency matrix

13) Extremal graph theory

Syllabus of tutorials:

Study Objective:

Knowledge:

Notions of graph theory, their basic properties and mutual relations.

Abilities:

Application of the theory in modelling and solving of particular questions and tasks.

Study materials:

References:

[1] J.A. Bondy, U.S.R. Murty. Graph theory.

Graduate Texts in Mathematics 244. Springer, New York, (2008).

Recommended references:

[2] R. Diestel. Graph theory.

Graduate Texts in Mathematics 173. Springer-Verlag, Berlin, (2005).

[3] L. Lovasz, M.D. Plummer. Matching Theory. North-Holland Publishing Co., Amsterdam, (1986).

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• FNSPE Prospectus MGR level (!)