On the Number of Perfect Matchings in Random Lifts

@article{Greenhill2010OnTN,
  title={On the Number of Perfect Matchings in Random Lifts},
  author={Catherine S. Greenhill and Svante Janson and Andrzej Rucinski},
  journal={Combinatorics, Probability & Computing},
  year={2010},
  volume={19},
  pages={791-817}
}
Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint) and replacing each edge by a randomly chosen perfect matching between the n-sets corresponding to the endpoints of the edge. Let XG be the number of perfect matchings in a random… CONTINUE READING