On the Number of Matchings in Regular Graphs

dc.contributor.authorShmuel Friedland
dc.contributor.authorElliot Krop
dc.contributor.authorKlas Markstrom
dc.description.abstractFor the set of graphs with a given degree sequence, consisting of any number of $2's$ and $1's$, 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 $m\le 4$.
dc.titleOn the Number of Matchings in Regular Graphs
dc.typeJournal Article, Academic Journal
dcterms.bibliographicCitationElectronic Journal of Combinatorics 15(R110), 45319, (August 31, 2008)