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A new characterization for parity graphs and a coloring problem with costs

  • Klaus Jansen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)

Abstract

In this paper, we give a characterization for parity graphs. A graph is a parity graph, if and only if for every pair of vertices all minimal chains joining them have the same parity. We prove that G is a parity graph, if and only if the Cartesian product G×K 2 is a perfect graph.

Furthermore, as a consequence we get a result for the polyhedron corresponding to an integer linear program formulation of a coloring problem with costs. For the case that the costs k v,3 =k v,c for each color c ≥ 3 and vertex v ∃ V, we show that the polyhedron contains only integral 0/1 extrema if and only if the graph G is a parity graph.

Keywords

Bipartite Graph Maximum Clique Coloring Problem Perfect Graph Integer Linear Program Formulation 
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 1998

Authors and Affiliations

  • Klaus Jansen
    • 1
  1. 1.Im StadtwaldMax-Planck Institut für InformatikSaarbrückenGermany

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