17-99 Paul Federbush

A New Property of Random Regular Bipartite Graphs (21K, LaTeX) Oct 1, 17

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Abstract. One deals with r-regular bipartite graphs with 2n vertices. In a previous paper Butera, Pernici, and the author have introduced a quantity d(i), a function of the number of i-matchings, and conjectured that as n goes to infinity the fraction of graphs that satisfy Delta^k d(i) > 0, for all k and i, approaches 1. Here Delta is the finite difference operator. In this paper it is proved that for each r, i, and k < 7 that the probability that Delta^k d(i) > 0 goes to 1 with n going to infinity. A formalism of Wanless as systematized by Pernici is central to the proof.

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