The Widom-Rowlinson model, the hard-core model and the extremality of the complete graph

European Journal of Combinatorics, pp. 70-76, 2017.

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Abstract:

Let HWR be the path on 3 vertices with a loop at each vertex. D. Galvin (Galvin, 2013, 2014) conjectured, and E. Cohen, W. Perkins and P. Tetali (Cohen et al., in press) proved that for any d-regular simple graph G on n vertices we have hom(G,HWR)≤hom(Kd+1,HWR)n/(d+1). In this paper we give a short proof of this theorem together with the ...More

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