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Ben Lund, Perfect matchings and derangements on graphs
Tuesday, January 19, 2021 @ 4:30 PM - 5:30 PM KST
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. This is joint work with Matija Bucic, Pat Devlin, Mo Hendon, and Dru Horne.