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Latin American Symposium on Theoretical Informatics

LATIN 1998: LATIN'98: Theoretical Informatics pp 249–260Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((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.

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Authors and Affiliations

  1. Im Stadtwald, Max-Planck Institut für Informatik, 66 123, Saarbrücken, Germany

    Klaus Jansen

Authors
  1. Klaus Jansen
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Editor information

Cláudio L. Lucchesi Arnaldo V. Moura

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© 1998 Springer-Verlag Berlin Heidelberg

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Jansen, K. (1998). A new characterization for parity graphs and a coloring problem with costs. In: Lucchesi, C.L., Moura, A.V. (eds) LATIN'98: Theoretical Informatics. LATIN 1998. Lecture Notes in Computer Science, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054326

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  • DOI: https://doi.org/10.1007/BFb0054326

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64275-6

  • Online ISBN: 978-3-540-69715-2

  • eBook Packages: Springer Book Archive

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