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, Ph.D. (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:
MA010/01: each even Wednesday 8:00–9:50 B410, 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
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
Teacher's information
http://www.fi.muni.cz/~hlineny/Vyuka/TG.html
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, 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 2008, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2008/MA010