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On the Fractional Chromatic Number of Monotone Self-dual Boolean Functions

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Frontiers in Algorithmics (FAW 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4613))

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Abstract

We compute the exact fractional chromatic number for several classes of monotone self-dual Boolean functions. We characterize monotone self-dual Boolean functions in terms of the optimal value of a LP relaxation of a suitable strengthening of the standard IP formulation for the chromatic number. We also show that determining the self-duality of monotone Boolean function is equivalent to determining feasibility of a certain point in a polytope defined implicitly.

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Authors and Affiliations

  1. University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada

    Daya Ram Gaur

  2. Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan

    Kazuhisa Makino

Authors
  1. Daya Ram Gaur
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  2. Kazuhisa Makino
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Franco P. Preparata Qizhi Fang

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© 2007 Springer-Verlag Berlin Heidelberg

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Gaur, D.R., Makino, K. (2007). On the Fractional Chromatic Number of Monotone Self-dual Boolean Functions. In: Preparata, F.P., Fang, Q. (eds) Frontiers in Algorithmics. FAW 2007. Lecture Notes in Computer Science, vol 4613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73814-5_14

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  • DOI: https://doi.org/10.1007/978-3-540-73814-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73813-8

  • Online ISBN: 978-3-540-73814-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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