MA051 Advanced topics in Graph Theory: Graphs on surfaces

Faculty of Informatics
Spring 2006
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Thu 14:00–15:50 B411 and each even Thursday 16:00–17:50 B411
Prerequisites
Usual basic knowledge of discrete mathematics and graphs. (See the book "Invitation to discrete mathematics".) Introductory knowledge of topology is also welcome.
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 50 student(s).
Current registration and enrolment status: enrolled: 0/50, only registered: 0/50, only registered with preference (fields directly associated with the programme): 0/50
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
Planar graphs, and more generaly graphs drawn on surfaces, play a (somehow surprisingly) important role in graph theory and in its applications. (For instance, the Four Colour theorem, the Graph Minor project, or various new efficient parametrized algorithms for hard graph problems.)
This subject introduces a mathematician or a theoretical computer scientist into the beauties of this branch of graph theory, often called topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
Syllabus
  • Basic graph terms, planar graphs, colourings.
  • The Kuratowski Theorem, with a proof.
  • The Four Colour Theorem, with an outline of a proof.
  • Planarity algorithms and complexity.
  • Graphs embedded on higher surfaces.
  • Graph minors, tree-width, and "forbidden" characterizations.
  • The "Kuratowski" theorem for any surface.
  • (A graph view of surface classification.)
  • Graphs drawings with edge-crossings. The crossing number.
  • Complexity of the graph crossing number problem.
  • Crossing-critical graphs and their structure.
Literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
  • NEŠETŘIL, Jaroslav and Jiří MATOUŠEK. Invitation to discrete mathematics. Oxford: Clarendon Press, 1998, xv, 410 s. ISBN 0-19-850207-9. info
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. Vyd. 2., opr. Praha: Karolinum, 2000, 377 s. ISBN 8024600846. info
Assessment methods (in Czech)
Written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Further Comments
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AGTT.html
The course is also listed under the following terms Spring 2008, Spring 2010, Spring 2012, Spring 2014.
  • Enrolment Statistics (Spring 2006, recent)
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