Ela Results and Open Problems in Matchings in Regular Graphs

@inproceedings{Friedland2012ElaRA,
  title={Ela Results and Open Problems in Matchings in Regular Graphs},
  author={Shmuel Friedland},
  year={2012}
}
This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower bounds we first survey the known results for bipartite graphs, and their continuous versions as the van der Waerden and Tverberg permanent conjectures and its variants. We then discuss non-bipartite graphs. Little is known beyond the recent proof of the Lovász… CONTINUE READING