The chromatic number of sparse colored mixed graphs

Amanda Montejano (1) , Alexandre Pinlou (2) , André Raspaud (3) , Eric Sopena (3)

1 Applied Mathematics IV Department
2 ALGCO - Algorithmes, Graphes et Combinatoire
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A colored mixed graph has vertices linked by both colored arcs and colored edges. The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (arc-color preserving) homomorphism from G to H. We study in this paper the colored mixed chromatic number of planar graphs, partial 2-trees and outerplanar graphs with given girth.

Domains: Discrete Mathematics [cs.DM]

Amanda Montejano, Alexandre Pinlou, André Raspaud, Eric Sopena. The chromatic number of sparse colored mixed graphs. EuroComb: European Conference on Combinatorics, Graph Theory and Applications, Sep 2009, Bordeaux, France. pp.363-367, ⟨10.1016/j.endm.2009.07.060⟩. ⟨hal-00409025⟩