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.