MA010 Graph Theory

Faculty of Informatics
Autumn 2010
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, Ph.D. (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:
MA010/01: each even Thursday 8:00–9:50 B410, J. Bouda
MA010/02: each odd Thursday 8:00–9:50 B410, J. Bouda
MA010/03: each even Tuesday 12:00–13:50 B003, R. Ganian
MA010/04: each odd Tuesday 12:00–13:50 B003, P. Hliněný
MA010/05: each even Tuesday 18:00–19:50 B011, R. Ganian
MA010/06: each odd Tuesday 18:00–19:50 B011, 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
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 targetted 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.
  • 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.
  • Network flows. The "max-flow min-cut" theorem via Ford-Fulkerson algorithm. Applications to matching and representatives.
  • 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
    required literature
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Invitation to discrete mathematics. 2nd ed. Oxford: Oxford University Press, 2009, xvii, 443. ISBN 9780198570431. info
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
    not specified
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Invitation to discrete mathematics. Oxford: Clarendon Press, 1998, xv, 410. ISBN 0198502087. info
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007, 423 s. ISBN 9788024614113. info
Teaching methods
MA010 is taught 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
Teacher's information
https://is.muni.cz/auth/el/1433/podzim2010/MA010/index.qwarp
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2010, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2010/MA010