Skip to content

CSM

Seminar

Maps and graphs on surfaces

Thomassen, C (Technical University of Denmark)
Monday 02 June 2008, 17:00-18:00

Seminar Room 1, Newton Institute

Abstract

Graph coloring is a extensively studied subject, partly because of its relation to optimization (time table problems). One of the main sources of inspiration was the 4 Color Problem (now a theorem). In 1890 Heawood considered the analogue for higher surfaces. This problem, known as the Heawood map color theorem, was settled by Ringel and Youngs in 1968. For example, the number of colors needed in the projective plane and the Klein bottle is 6. For the torus it is 7, etc. Although these numbers tend to infinity, there is a 5 color theorem for each surface in the following sense: For every surface S, there exist a finite number of (forbidden) graphs such that an arbitrary graph on S can be 5-colored if and only if it does not contain one of the forbidden graph as a subgraph. There is no 4-color theorem of this type. In the talk these and related results will be discussed.

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧