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The mutual exclusion scheduling problem for permutation and comparability graphs

  • Algorithms and Data Structures III
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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph G and a fixed constant m, the problem is to find a minimum coloring of G such that each color is used at most m times. The complexity of this problem for comparability graphs was mentioned as an open problem by Möhring (1985) and for permutation graphs (a subclass of comparability graphs) as an open problem by Lonc (1991). We prove that this problem is already NP-complete for permutation graphs and for each fixed constant m ≥ 6.

This work was done while the author was associated with the University Trier and supported in part by DIMACS and by EU ESPRIT LTR Project No. 20244 (ALCOM-IT).

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Authors and Affiliations

  1. Max Planck Institute for Computer Science, Im Stadtwald, 66 123, Saarbrücken, Germany

    Klaus Jansen

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  1. Klaus Jansen
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Jansen, K. (1998). The mutual exclusion scheduling problem for permutation and comparability graphs. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028568

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  • DOI: https://doi.org/10.1007/BFb0028568

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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