On the Number of Matchings in Regular Graphs

@article{Friedland2008OnTN,
  title={On the Number of Matchings in Regular Graphs},
  author={Shmuel Friedland and E. Krop and Klas Markstr{\"o}m},
  journal={Electr. J. Comb.},
  year={2008},
  volume={15}
}
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… CONTINUE READING