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Enumeration of perfect matchings of lattice graphs by Pfaffians

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  • Feng, Xing
  • Zhang, Lianzhu
  • Zhang, Mingzu

Abstract

Enumeration of perfect matchings in general graphs (even in bipartite graphs) is #P-complete. In this paper, we obtain explicit expressions of the number of perfect matchings of 8.6.4 lattices with toroidal boundary by enumerating Pfaffians.

Suggested Citation

  • Feng, Xing & Zhang, Lianzhu & Zhang, Mingzu, 2018. "Enumeration of perfect matchings of lattice graphs by Pfaffians," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 412-420.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:412-420
    DOI: 10.1016/j.amc.2018.06.027
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    References listed on IDEAS

    as
    1. Yan, Weigen & Yeh, Yeong-Nan & Zhang, Fuji, 2008. "Dimer problem on the cylinder and torus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6069-6078.
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