MA051 Advanced Graph Theory: Topological

Faculty of Informatics
Spring 2012
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.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Tue 13:00–15:50 G191m
Prerequisites
Graph Theory MA010. 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 30 student(s).
Current registration and enrolment status: enrolled: 0/30, only registered: 0/30, only registered with preference (fields directly associated with the programme): 0/30
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
This subject introduces a mathematician or a theoretical computer scientist into the beauties of the 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.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • Basic graph terms, basics of topology.
  • Jordan's curve theorem, with a proof.
  • Kuratowski's 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.
  • Graphs drawings with edge-crossings. The crossing number problem, complexity.
  • Crossing-critical graphs and their structure.
Literature
    required literature
  • MOHAR, Bojan and Carsten THOMASSEN. Graphs on Surfaces. Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/stud-en.html#spring
The course is also listed under the following terms Spring 2006, Spring 2008, Spring 2010, Spring 2014.
  • Enrolment Statistics (Spring 2012, recent)
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