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Journal of Combinatorial Optimization

, Volume 23, Issue 1, pp 79–93 | Cite as

On backbone coloring of graphs

  • Weifan WangEmail author
  • Yuehua Bu
  • Mickaël Montassier
  • André Raspaud
Article

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 uvE(H) and |f(u)−f(v)|≥1 if uvE(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=TC 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 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Weifan Wang
    • 1
    Email author
  • Yuehua Bu
    • 1
  • Mickaël Montassier
    • 2
  • André Raspaud
    • 2
  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  2. 2.LaBRI UMR CNRS 5800Universite Bordeaux ITalence CedexFrance

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