Enumeration of perfect matchings of lattice graphs by Pfaffians

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摘要

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.

论文关键词：Perfect matching,8.6.4 lattice graph,Pfaffian graph,Toroidal boundary

论文评审过程：Received 8 December 2017, Revised 5 June 2018, Accepted 10 June 2018, Available online 11 July 2018, Version of Record 11 July 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.06.027