On the Number of Matchings in Regular Graphs

نویسندگان

Shmuel Friedland

E. Krop

Klas Markström

چکیده

For the set of graphs with a given degree sequence, consisting of any number of 2s and 1s, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of m-matchings. We find the expected value of the number of m-matchings of r-regular bipartite graphs on 2n vertices with respect to the two standard measures. We state and discuss the conjectured upper and lower bounds for m-matchings in r-regular bipartite graphs on 2n vertices, and their asymptotic versions for infinite r-regular bipartite graphs. We prove these conjectures for 2-regular bipartite graphs and for m-matchings with m ≤ 4.

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