On backbone coloring of graphs

Weifan Wang (), Yuehua Bu (), Mickaël Montassier () and André Raspaud ()
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Weifan Wang: Zhejiang Normal University
Yuehua Bu: Zhejiang Normal University
Mickaël Montassier: Universite Bordeaux I
André Raspaud: Universite Bordeaux I

Journal of Combinatorial Optimization, 2012, vol. 23, issue 1, No 7, 79-93

Abstract: 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)→{1,2,…,k} such that |f(u)−f(v)|≥2 if uv∈E(H) and |f(u)−f(v)|≥1 if uv∈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∪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.

Keywords: Backbone coloring; Halin graph; Maximum average degree; Spanning tree; Hamiltonian path (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-010-9342-6

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