On backbone coloring of graphs

Authors:
Weifan Wang;Yuehua Bu;Mickaël Montassier;André Raspaud
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua, China 321004;Department of Mathematics, Zhejiang Normal University, Jinhua, China 321004;LaBRI UMR CNRS 5800, Universite Bordeaux I, Talence Cedex, France 33405;LaBRI UMR CNRS 5800, Universite Bordeaux I, Talence Cedex, France 33405
Venue:
Journal of Combinatorial Optimization
Year:
2012

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Abstract

Let G be a graph and H a subgraph of G. A backbone-k-coloring of (G,H) is a mapping f: V(G)驴{1,2,驴,k} such that |f(u)驴f(v)|驴2 if uv驴E(H) and |f(u)驴f(v)|驴1 if uv驴E(G)\E(H). The backbone chromatic number of (G,H) is the smallest integer k such that (G,H) has a backbone-k-coloring. In this paper, we characterize the backbone chromatic number of Halin graphs G=T驴C with respect to given spanning trees T. Also we study the backbone coloring for other special graphs such as complete graphs, wheels, graphs with small maximum average degree, graphs with maximum degree 3, etc.