On the Number of Matchings in Regular Graphs
| dc.creator | Friedland, S. | |
| dc.creator | Krop, E. | |
| dc.creator | Markström, K. | |
| dc.date | 2008-01-15 | |
| dc.date.accessioned | 2026-07-07T08:54:33Z | |
| dc.date.available | 2026-07-07T08:54:33Z | |
| dc.description | 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 $2n$ 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.description | 26 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0801.2256 | |
| dc.identifier | http://arxiv.org/abs/0801.2256 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145973 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05A16, 05C70,05C80, 82B20 | |
| dc.title | On the Number of Matchings in Regular Graphs | |
| dc.type | text |