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FI:MA010 Graph Theory - Course Information

## MA010 Graph Theory

**Faculty of Informatics**

Autumn 2011

**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)

doc. Mgr. Jan Obdržálek, PhD. (assistant) **Guaranteed by**- prof. RNDr. Mojmír Křetínský, CSc.

Department of Computer Science - Faculty of Informatics

Contact Person: prof. RNDr. Petr Hliněný, Ph.D. **Timetable**- Wed 8:00–9:50 D3
- Timetable of Seminar Groups:

*P. Hliněný*

MA010/01: each even Wednesday 18:00–19:50 B204,*J. Bouda*

MA010/02: each odd Wednesday 18:00–19:50 B204,*J. Bouda*

MA010/03: each even Thursday 16:00–17:50 G101,*J. Bouda*

MA010/04: each odd Thursday 16:00–17:50 G101,*J. Bouda*

MA010/05: each even Friday 10:00–11:50 G125,*R. Ganian*

MA010/06: each odd Friday 10:00–11:50 G125,*R. Ganian*

MA010/07: each even Friday 12:00–13:50 G125,*R. Ganian* **Prerequisites**- !
**PřF:M5140**Graph Theory &&! NOW (**PřF:M5140**Graph Theory )

Basic mathematics, sets, relations, induction (roughly corresponding to the mathematical parts of IB000). **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 23 fields of study the course is directly associated with, display
**Course objectives**- This is a standard course in graph theory.
Basic concepts, graph properties (with simplified proofs), formulations of usual graph problems, and abstract-level algorithms for their solving, are presented. Although the content of this course is targeted at CS students, it is accessible also to others.

At the end of the course, successful students shall understand in depth and tell all the basic terms of graph theory; be able to reproduce the proofs of some fundamental statements on graphs; be able to solve new simple problems; and be ready to apply this knowledge in (especially) computer science applications. **Syllabus**- Graphs and relations. Subgraphs, isomorphism, degrees. Directed graphs.
- Graph connectivity and basic searching. Multiple connectivity, edge-connectivity. Eulerian graphs.
- Distance in graphs, graph metrics, weighted distance. Basic approaches to computing distance.
- Network flows. The "max-flow min-cut" theorem via Ford-Fulkerson algorithm. Applications to matching and representatives.
- Trees and their characterizations, tree isomorphism, rooted trees. Spanning trees, enumeration.
- Spanning trees and the MST problem. Greedy algorithms. Matroids and their relation to graphs and greedy algorithms.
- Graph colouring, bipartite graphs and their recognition, edge and list colourings. Independent set, clique, vertex cover, Hamiltonian, etc problems.
- Planar embeddings of graphs, Euler formula and its applications. Planar graph colouring. Graph drawing.
- Selected advanced topics (time allowing): Intersection graph representations, chordal graphs, structural width measures, graph minors, embedding on surfaces, crossing number, Ramsey theory.

**Literature**- HLINĚNÝ, Petr. Základy teorie grafů.
*Elportál*. Brno: Masarykova univerzita, 2010. ISSN 1802-128X.*URL*info - MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Invitation to discrete mathematics*. 2nd ed. Oxford: Oxford University Press, 2009. xvii, 443. ISBN 9780198570431. info

*required literature*- MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Kapitoly z diskrétní matematiky*. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007. 423 s. ISBN 9788024614113. info

*not specified*- HLINĚNÝ, Petr. Základy teorie grafů.
**Teaching methods**- MA010 is taught in weekly 2-hour lectures, with bi-weekly 2-hour compulsory tutorials. Since this is a mathematical subject, the students are expected to learn the given theory and be able to understand and compose mathematical proofs. Memorizing is not enough! All the study materials, demonstrations, and study agenda are presented through the online IS syllabus.
**Assessment methods**- The resulting grade is taken from a term test (20%), voluntary bonus work (arbitrary), and a final written exam (80%). The written semester test for 20 points can be repeated (corrected) once, and at least 10 point score is strictly required before the final exam. Possible bonus points and penalties for not attending the compulsory tutorials count towards this limit. The final written exam for 80 points consists of a 40 point part about basic graph terms and their applications, and a 40 point advanced part in which students have to come with solutions and proofs of rather difficult problems. More then 50 points in total is required to pass.
**Language of instruction**- English
**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**- https://is.muni.cz/auth/el/1433/podzim2011/MA010/index.qwarp

- Enrolment Statistics (Autumn 2011, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2011/MA010