Graph theory and combinatorics
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| NI-GAK | Z,ZK | 5 | 2P+2C | Czech |
- Course guarantor:
- Tomáš Valla
- Lecturer:
- Michal Opler
- Tutor:
- Michal Dvořák
- Supervisor:
- Department of Theoretical Computer Science
- Synopsis:
-
The goal of the class is to introduce the most important topics in graph theory, combinatorics, combinatorial structures, discrete models and algorithms. The emphasis will be not only on undestanding the basic principles but also on applications in problem solving and algorithm design. The topics include: generating functions, selected topics from graph and hypergraph coloring, Ramsey theory, introduction to probabilistic method, properties of various special classes of graphs and combinatorial structures. The theory will be also applied in the fields of combinatorics on words, formal languages and bioinformatics.
- Requirements:
-
We expect knowledge of topics from the courses Algorithms and graphs I. and II. (BI-AG1, BI-AG2).
- Syllabus of lectures:
-
List of the topics
1. Generating functions
2. Graph coloring and perfect graphs
3. Introduction to Ramsey theory
4. Matching in general graphs
5. Counting spanning trees
6. Introduction to probabilistic method
7. Extremal combinatorics
8. Planar graphs and Kuratowski theorem
9. Coloring graphs on surfaces
10. List coloring and choosability
11. Edge coloring
12. Combinatorial games
- Syllabus of tutorials:
-
1. Generating functions
2. Graph coloring and perfect graphs
3. Introduction to Ramsey theory
4. Matching in general graphs
5. Counting spanning trees
6. Introduction to probabilistic method
7. Extremal combinatorics
8. Planar graphs and Kuratowski theorem
9. Coloring graphs on surfaces
10. List coloring and choosability
11. Edge coloring
12. Combinatorial games
- Study Objective:
- Study materials:
-
1. Bollobas, B. : Modern Graph Theory. Springer, 1998. ISBN 0-387-98488-7.
2. Graham, R. L. - Knuth, D. - Patashnik, O. : Concrete Mathematics. Addison-Wesley, 1994. ISBN 978-0-201-55802-9.
- Note:
- Further information:
- https://courses.fit.cvut.cz/NI-GAK/
- Time-table for winter semester 2024/2025:
- Time-table is not available yet
- Time-table for summer 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
Mon Tue Wed Thu Fri - The course is a part of the following study plans:
-
- Master specialization Computer Security, in Czech, 2020 (elective course)
- Master specialization Design and Programming of Embedded Systems, in Czech, 2020 (elective course)
- Master specialization Computer Systems and Networks, in Czech, 202 (elective course)
- Master specialization Management Informatics, in Czech, 2020 (elective course)
- Master specialization Software Engineering, in Czech, 2020 (elective course)
- Master specialization System Programming, in Czech, version from 2020 (elective course)
- Master specialization Web Engineering, in Czech, 2020 (elective course)
- Master specialization Knowledge Engineering, in Czech, 2020 (elective course)
- Master specialization Computer Science, in Czech, 2020 (PS)
- Mgr. programme, for the phase of study without specialisation, ver. for 2020 and higher (VO)
- Master Specialization Digital Business Engineering, 2023 (VO)
- Master specialization System Programming, in Czech, version from 2023 (elective course)
- Master specialization Computer Science, in Czech, 2023 (PS)