Perfect matchings and derangements on graphs. Issue 2 (6th January 2021) - Bucic, Matija; Devlin, Pat; Hendon, Mo; Horne, Dru; Lund, Ben
Abstract: We show that each perfect matching in a bipartite graph G intersects at least half of the perfect matchings in G . This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of derangements and permutations on graphs. We give several related results and open questions.