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On the number of matching in regular graphs
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2008 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 15, no 1Article in journal (Refereed) Published
Abstract [en]

For 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 veritces 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.

Place, publisher, year, edition, pages
2008. Vol. 15, no 1
Keyword [en]
partial matching and asymptotic growth of average matchings for r-regular bipartite graphs, asymptotic matching conjectures
National Category
Discrete Mathematics
URN: urn:nbn:se:umu:diva-52123ISI: 000258830300003OAI: diva2:497230
343CN Times Cited:3 Cited References Count:15Available from: 2012-02-10 Created: 2012-02-10 Last updated: 2012-02-10

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