Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, January 25, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Robert Berke

The Morphism Chromatic Number - Between Layouts and Colorings

A layout of a graph G is a bijective function psi: V(G) -> [n], n denoting the number of vertices of G. The cost of a layout can be defined to be sum_{uv in E(G)} |psi(u)-psi(v)|. A proper k-coloring of G is a function chi: V(G) -> [k] such that for every edge uv in G, chi(u) eq chi(v) is satisfied.

We define the morphism chromatic number, a new graph parameter that combines aspects of layouts and colorings of a graph. The minimum morphism cost of a graph is min_k {min_{phi: V(G) -> [k]} sum_{uv in E (G)} |phi(u)-phi(v)|}, with phi being a proper coloring. The morphism chromatic number is the minimum value k for which the minimum morphism cost is attained.

In this talk we overview results on the morphism chromatic number for several graph classes. Also we show that deciding whether a graph has a certain morphism chromatic number is NP-hard.

Joint work with Dieter Mitsche.

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