Corpus ID: 232240668

Counting and Sampling Perfect Matchings in Regular Expanding Non-Bipartite Graphs

@article{Ebrahimnejad2021CountingAS,
  title={Counting and Sampling Perfect Matchings in Regular Expanding Non-Bipartite Graphs},
  author={Farzam Ebrahimnejad and Ansh Nagda and Shayan Oveis Gharan},
  journal={ArXiv},
  year={2021},
  volume={abs/2103.08683}
}
We show that the ratio of the number of near perfect matchings to the number of perfect matchings in d-regular strong expander (non-bipartite) graphs, with 2n vertices, is a polynomial in n, thus the Jerrum and Sinclair Markov chain [JS89] mixes in polynomial time and generates an (almost) uniformly random perfect matching. Furthermore, we prove that such graphs have at leastΩ(d)n many perfect matchings, thus proving the Lovasz-Plummer conjecture [LP86] for this family of graphs. ∗febrahim@cs… Expand

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