CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Graph Theory

Code Completion Credits Range Language
XP01TGR ZK 4 2P+1S Czech
Garant předmětu:
Marie Demlová
Lecturer:
Marie Demlová
Tutor:
Marie Demlová
Supervisor:
Department of Mathematics
Synopsis:

Basic course in graph theory. Trees, their characterization, minimal spanning tree. Strongly connected components, rooted trees. Shortest paths, Floyds algorithm. Euler graphs and their applications, Hamiltonian graphs and their applications. Chvatal's theorem. Flow in networsk, admissible flows and admissible circulations. Matchings in general graphs and in bipartite graphs. Vertex cover and independent sets. Cliques. Colorings. Plannar graphs. Graphs and vector spaces. The content of the course is modified according to the needs of students.

Requirements:

No.

Syllabus of lectures:

1. Basic notions and properties concerning undirected graphs.

2. Vertex connectivity a edge connectivity, cut vertices, bridges.

3. Basic notions and propertis concerning directed graphs.

4. Transitive closure and transitive reduction of difectec graphs, minimally strongly connected graphs.

5. Hamiltonian graphs (undirected, directed), Chvatal's theorem.

6. Flow in networks. Ford-Fulkerson Theorem. Bases of fast algorithms for finding maximal flow in a network.

8. Matching in general graphs and in bipartite graphs.

9. Independent sets, cliques, vertex covers.

10. Edge covers. Colorability with emphasis to vertex colorings.

11. Graphs and vector spaces. Circiut vector subspace and cut vector subspace.

12. Duality. Duality based on plannar graphs is the same notions as duality

arising from circuits and cuts.

Syllabus of tutorials:

Excerices have the form of homeworks with consultations.

Study Objective:

The main goal of the course is to introduce to students methods and techniques used in graph theory. Emphasis is given to self study; during semestr students get small task to be solved and the solution correctly written together with its justification.

Study materials:

1. Reinhard Diestel: Graph Theory. Springer-Verlag, New York, 1997.

2. M.N.S. Swamy, K. Thulasiraman: Graphs, Networks, and Algorithms, Part 1, Graph Theory, John Wiley &amp; Sons, New York, 1981

Note:
Further information:
https://moodle.fel.cvut.cz/courses/XP01TGR
Time-table for winter semester 2024/2025:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomT2:C2-83Demlová M.08:15–09:00(lecture parallel1parallel nr.101)DejvicecvičebnaroomT2:C2-83Demlová M.09:15–10:45(lecture parallel1)Dejvicecvičebna
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet11506804.html