A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs

  • Krzysztof Giaro
  • Robert Janczewski
  • Marek Kubale
  • Michał Małafiejski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2462)


We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Crmatic Sum Problem is NP-complete on planar bipartite graphs with ∇≤ 5, but polynomial on bipartite graphs with ∇≤ 3, for which we construct an O(n 2)-time algorithm. Hence, we tighten the borderline of intractability for this problem on bipartite graphs with bounded degree, namely: the case ∇ = 3 is easy, ∇ = 5 is hard. Moreover, we construct a 27/26-approximation algorithm for this problem thus improving the best known approximation ratio of 10/9.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Krzysztof Giaro
    • 1
  • Robert Janczewski
    • 1
  • Marek Kubale
    • 1
  • Michał Małafiejski
    • 1
  1. 1.Foundations of Informatics DepartmentGdańsk University of TechnologyPoland

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