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Efficient Algorithms for Weighted Colorings of Series-Parallel Graphs

  • Xiao Zhou
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

Abstract

Let G be a weighted graph such that each vertex v has a positive integer weight \( w\left( v \right) \) . A weighted coloring of G is to assign a set of \( w\left( v \right) \) colors to each vertex \( v \) so that any two adjacent vertices receive disjoint sets of colors. This paper gives an efficient algorithm to find the minimum number of colors required for a weighted coloring of a given series-parallel graph G in time \( O\left( {nw_{max} } \right) \) , where n is the number of vertices and \( w_{max} \) is the maximum vertex-weight of G.

Keywords

Weighted Graph Parallel Connection Perfect Graph Preemptive Schedule Minimum Completion Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Xiao Zhou
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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