Enumeration of Perfect Matchings in Graphs with Reflective Symmetry

@article{Ciucu1997EnumerationOP,
  title={Enumeration of Perfect Matchings in Graphs with Reflective Symmetry},
  author={Mihai Ciucu},
  journal={J. Comb. Theory, Ser. A},
  year={1997},
  volume={77},
  pages={67-97}
}
A plane graph is called symmetric if it is invariant under the reflection across some straight line. We prove a result that expresses the number of perfect matchings of a large class of symmetric graphs in terms of the product of the number of matchings of two subgraphs. When the graph is also centrally symmetric, the two subgraphs are isomorphic and we obtain a counterpart of Jockusch’s squarishness theorem. As applications of our result, we enumerate the perfect matchings of several families… CONTINUE READING
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