Introduction to Graph Theory B

Lecturer:

Petr Ambrož (gar.)

Tutor:

Petr Ambrož (gar.), František Jahoda

Supervisor:

Department of Mathematics

Synopsis:

The course provides an explanation of modern graph theory, applications and algorithms are discussed.

Requirements:

Syllabus of lectures:

1) Basic notion of graph theory

2) Connectivity

3) Bipartite graphs

4) Forests and trees

5) Spanning tree, minimal spanning tree

6) Euler cycles and Hamilton circles

7) Maximal and perfect matching

8) Edge colouring

9) Flows in networks

10) Vertex colouring

11) Planar graphs

Syllabus of tutorials:

1) Depth-first and breadth-first search

2) Shortest path in a graph (Dijkstra, A*, Floyd-Warhsall)

3) Minimal spannig thee (Kruskal algoritm)

4) Maximal flow in a network (Ford-Fulkerson)

5) Maximál matching (Edmonds algoritm)

6) Planarity algorithm

Study Objective:

Knowledge:

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

Abilities:

Application of the theory in modelling and solving of particular questions and tasks, including computer implementation.

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] J. Matoušek and J. Nešetřil. Kapitoly z diskrétní matematiky. MatfyzPress,

1996.

[3] Ján Plesník. Grafové algoritmy.

Veda, Bratislava, (1983).

Teaching tools:

Computer lab (Windows/Unix) with Python and C++.

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: