Geodesic
On the number of matchings in regular graphs
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl arXiv EuDML
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 $m\le 4$.
DOI : 10.37236/834
Classification : 05A15, 05A16, 05C70, 05C80, 82B20
Mots-clés : partial matching and asymptotic growth of average match- 
S. Friedland; E. Krop; K. Markström. On the number of matchings in regular graphs. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/834
@article{10_37236_834,
     author = {S. Friedland and E. Krop and K. Markstr\"om},
     title = {On the number of matchings in regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/834},
     zbl = {1181.05011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/834/}
}
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