Paul Federbush
A New Property of Random Regular Bipartite Graphs
(21K, LaTeX)
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.