#
FI:MA010 Graph Theory - Course Information

## MA010 Graph Theory

**Faculty of Informatics**

Autumn 2014

**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)

Frédéric Dupont Dupuis, Ph.D. (seminar tutor)

Sebastian Ordyniak, PhD (seminar tutor)

Mgr. Michal Kotrbčík, Ph.D. (assistant)

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.

Supplier department: Department of Computer Science - Faculty of Informatics **Timetable**- Thu 8:00–9:50 D1
- Timetable of Seminar Groups:

*F. Dupont Dupuis*

MA010/02: each odd Monday 12:00–13:50 A217,*F. Dupont Dupuis*

MA010/03: each even Monday 16:00–17:50 A217,*F. Dupont Dupuis*

MA010/04: each odd Monday 16:00–17:50 A217,*F. Dupont Dupuis*

MA010/05: each even Monday 16:00–17:50 C525,*S. Ordyniak*

MA010/06: each odd Monday 16:00–17:50 C525,*S. Ordyniak*

MA010/07: each even Monday 10:00–11:50 A318,*S. Ordyniak*

MA010/08: each odd Monday 10:00–11:50 A318,*S. Ordyniak* **Prerequisites**- !
**PřF:M5140**Graph Theory &&! NOW (**PřF:M5140**Graph Theory )

Discrete mathematics, basic concepts of graphs and graph algorithms. IB000 (or equivalent from other schools) is highly recommended. **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 200 student(s).

Current registration and enrolment status: enrolled:**0**/200, only registered:**0**/200, only registered with preference (fields directly associated with the programme):**0**/200 **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.
All standard 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 graph 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 searching, multiple connectivity. Trees, the MST problem.
- Distance in graphs, graph metrics, concepts of route planning in graphs.
- Network flows. The "max-flow min-cut" theorem via Ford-Fulkerson algorithm. Applications to connectivity, matching and representatives.
- Matching in graphs, packing problems, enumeration.
- Graph colouring, edge and list colourings.
- Computationally hard graph problems: independent set, clique, vertex cover, Hamiltonian, etc.
- Planar embeddings of graphs, Euler formula and its applications. Graph drawing.
- Selected advanced topics (time allowing): Intersection graph representations, chordal graphs, structural width measures, graph minors, graph embeddings on surfaces, crossing number, Ramsey theory.

**Literature**- HLINĚNÝ, Petr. Základy teorie grafů.
*Elportál*. Brno: Masarykova univerzita, 2010. ISSN 1802-128X.*URL*info

*required literature*- MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Invitation to discrete mathematics*. 2nd ed. Oxford: Oxford University Press, 2009. xvii, 443. ISBN 9780198570431. info - MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Kapitoly z diskrétní matematiky*. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007. 423 s. ISBN 9788024614113. info

*recommended literature*- 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/podzim2014/MA010/index.qwarp

- Enrolment Statistics (Autumn 2014, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2014/MA010