A Collection of MTA–ELTE GAC manuscripts
نویسندگان
چکیده
LetHWR be the path on 3 vertices with a loop at each vertex. D. Galvin [4, 5] conjectured, and E. Cohen, W. Perkins and P. Tetali [2] proved that for any d-regular simple graph G on n vertices we have hom(G,HWR) ≤ hom(Kd+1, HWR) . In this paper we give a short proof of this theorem together with the proof of a conjecture of Cohen, Perkins and Tetali [2]. Our main tool is a simple bijection between the Widom-Rowlinson model and the hard-core model on another graph. We also give a large class of graphs H for which we have hom(G,H) ≤ hom(Kd+1, H) . In particular, we show that the above inequality holds if H is a path or a cycle of even length at least 6 with loops at every vertex.
منابع مشابه
A Collection of MTA–ELTE GAC manuscripts
There are two known families of maximum scattered Fq-linear sets in PG(1, q): the linear sets of pseudoregulus type and for t ≥ 4 the scattered linear sets found by Lunardon and Polverino. For t = 4 we show that these are the only maximum scattered Fq-linear sets and we describe the orbits of these linear sets under the groups PGL(2, q) and PΓL(2, q).
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تاریخ انتشار 2017