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ECTS Course Overview



Graph Theory

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-4302/02
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KOV16doc. Mgr. Petr Kovář, Ph.D.
ZAV0063Ing. Jakub Závada
Summary
The course covers both basic and advanced topics of Graph Theory, often overlapping with other branches of mathematics (algebra, combinatorics).
A mandatory part of the course is one or sometimes two projects focused on real life problems that are solved using methods of graph theory.
Learning Outcomes of the Course Unit
Each student is supposed to
- analyze real life problems
- express them as a graph theory problem
- solve the problem using graph theory methods
- give an interpretation of the theoretical results in the terms of the original problems
At the same time he should decide what are the limits of an ideal theoretical solution in contrast to the real situation.
Course Contents
Lectures:
1) Graphs, simple graphs. Incidence matrix and adjacency matrix. Subgraphs. Degree of a vertex.
2) Paths and cycles.
3) Trees, bridges and cuts.
4) Graph isomorphisms.
5) Connectivity and blocks. Cut sets.
6) Matching and covers in general and bipartite graphs. Perfect matchings.
7) Edge colorings. Chromatic index, Vizing's Theorem.
8) Vertex colorings, Chromatic number, Brook's Theorem.
9) Planar graphs. Dual graphs, Euler's formula for connected planar graphs, Kuratowski's Theorem. Four Color Theorem.
10) Non-planar graph, measures of non-planarity.
11) Eulerian and Hamiltonian graphs.
12) Oriented graphs. Oriented paths and cycles.
13) Tournaments, graph models.
14) Further topics: flows in networks, cuts.
Recommended or Required Reading
Required Reading:
J. Matoušek, J. Nešetřil, Chapters in Discrete Mathematics, Karolinum Praha (2000).
P. Kovář: Teorie grafů, VŠB (2011)
J. Matoušek, J. Nešetřil, Kapitoly z diskrétní matematiky, Karolinum Praha (2000).

Recommended Reading:
D. B. West, Introduction to graph theory - 2nd ed., Prentice-Hall, Upper Saddle River NJ, (2001).
D. B. West, Introduction to graph theory - 2nd ed., Prentice-Hall, Upper Saddle River NJ, (2001).
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Project work
Assesment methods and criteria
Tasks are not Defined