Combinatorial proof of the log-concavity of the sequence of matching numbers

For k greater than or equal to l we construct an injection from the set of pairs of matchings in a given graph G of sizes l - 1 and k + 1 into the set of pairs of matchings in G of sizes l and k. This provides a combinatorial proof of the log-concavity of the sequence of matching numbers of a graph. Besides, this injection implies that a certain weighted version of the matching numbers is strongly x-log-concave in the sense of Sagan. (C) 1996 Academic Press, Inc.