## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

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

Duration: This information is not available in the database

Location: CAB G51

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.

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996

Information for students and suggested topics for student talks