Předmět Advanced Graph Theory: Topological (MA051)

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Materiál	Typ	Datum	Počet stažení

Cíl

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.

Osnova

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.

Literatura

povinná literaturaMOHAR, Bojan a Carsten THOMASSEN. Graphs on Surfaces. : Johns Hopkins University Press, 2001. ISBN 0-8018-6689-8. URL info

Požadavky

Graph Theory MA010. Introductory knowledge of topology is also welcome.

Garant

prof. RNDr. Mojmír Křetínský, CSc.

Vyučující

prof. RNDr. Petr Hliněný, Ph.D.