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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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
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