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

Daya Ram Gaur,Kazuhisa Makino

doi:10.1007/978-3-540-73814-5_14

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

Daya Ram Gaur, Kazuhisa Makino

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

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Publication Date: Aug 1, 2007

Affiliation: University of Lethbridge, The University of Tokyo

#Boolean Functions In Terms #Fractional Chromatic Number + Show 8 more

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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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