On the fractional chromatic number of monotone self-dual boolean functions

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. © Springer-Verlag Berlin Heidelberg 2007.