#
FI:MA010 Graph Theory - Course Information

## MA010 Graph Theory

**Faculty of Informatics**

Autumn 2008

**Extent and Intensity**- 2/1. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Petr Hliněný, Ph.D. (lecturer)

doc. RNDr. Jan Bouda, Ph.D. (seminar tutor)

RNDr. Robert Ganian (seminar tutor) **Guaranteed by**- prof. RNDr. Mojmír Křetínský, CSc.

Faculty of Informatics

Contact Person: prof. RNDr. Petr Hliněný, Ph.D. **Timetable**- Thu 17:00–18:50 D1
- Timetable of Seminar Groups:

*J. Bouda*

MA010/02: each odd Wednesday 8:00–9:50 B410,*J. Bouda*

MA010/03: each even Thursday 14:00–15:50 B011,*P. Hliněný*

MA010/04: each odd Thursday 14:00–15:50 B011,*R. Ganian*

MA010/05: each even Friday 8:00–9:50 B003,*R. Ganian*

MA010/06: each odd Friday 8:00–9:50 B003,*R. Ganian* **Prerequisites**- !
**PřF:M5140**Graph Theory &&! NOW (**PřF:M5140**Graph Theory )

Basic mathematics, sets, relations, induction. **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.

The capacity limit for the course is 180 student(s).

Current registration and enrolment status: enrolled:**0**/180, only registered:**0**/180, only registered with preference (fields directly associated with the programme):**0**/180 **fields of study / plans the course is directly associated with**- there are 21 fields of study the course is directly associated with, display
**Course objectives**- This is an introductory course in graph theory.
Basic concepts, graph properties, formulation of simple graph problems, and simple efficient algorithms for their solving, are presented. Although the content of this course is targetted at CS students, it is accessible also to others.

Successful student shall understand all basic areas of graphs in mathematics, and be able to apply this knowledge in (especially) informatical applications. (S)He should also learn how to prove statements about graphs, and how to solve new graph problems uncovered in practical applications. **Syllabus**- Graphs and relations. Subgraphs, isomorphism, degrees, implementation. Directed graphs.
- Graph connectivity, algorithms for searching. Multiple connectivity, edge-connectivity. Eulerian graphs.
- Distance in graphs, Dijkstra's algorithm, graph metric and its computation.
- Trees and their characterizations, tree isomorphism, rooted trees.
- Greedy algorithm. Spanning trees, MST problem. Algorithms of Jarnik and Boruvka. Matroids.
- Network flows: formulation and applications to practical problems. Ford-Fulkerson's algorithm for maximal flow. Applications to matching and representatives.
- Graph colouring, bipartite graphs and their recognition. Independence, cliques, vertex cover, relevant hard algorithmic problems.
- Planar embeddings of graphs, Euler''s formula and its applications. Planar graph colouring. Crossing number.
- Selected advanced topics (time allowing): Intersection graph representations, chordal graphs, tree-width +, minors, embedding on surfaces and planar covers, graph drawing - "spring embedder".

**Literature**- Petr Hliněný, Teorie grafů,
http://www.fi.muni.cz/~hlineny/Vyuka/GT/Grafy-text07.pdf . - MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Kapitoly z diskrétní matematiky*. Vyd. 2., opr. Praha: Karolinum, 2000. 377 s. ISBN 8024600846. info - MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Invitation to discrete mathematics*. Oxford: Clarendon Press, 1998. xv, 410. ISBN 0198502087. info

- Petr Hliněný, Teorie grafů,
**Assessment methods**- This subject is taught in weekly lectures, with bi-weekly compulsory tutorials. It is a mathematical subject, and so the students are expected to learn the given theory and be able to understand and compose mathematical proofs.

The resulting grade is taken from a term test (20%), voluntary bonus work, and a final written exam (80%). **Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses**- PřF:
**M5140**Graph Theory

!M5145 && !(FI:MA010)

- PřF:
**Teacher's information**- http://www.fi.muni.cz/~hlineny/Vyuka/TG.html

- Enrolment Statistics (Autumn 2008, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2008/MA010