An extension of Kasteleyn's method of enumerating the 1-factors of planar graphs

CHC Little - … Mathematics: Proceedings of the Second Australian …, 1974 - Springer
CHC Little
Combinatorial Mathematics: Proceedings of the Second Australian Conference, 1974Springer
Throughout this paper, we let G be a finite, connected graph with no loops or multiple edges.
We denote the vertex set of G by V (G) and its edge set by E (G). A 1-factor of G is a set f of
edges such that for every v EV (G) exactly one edge of f is incident on v. Kasteleyn [1] has
introduced a technique for using Pfaffians to enumerate the 1-factors of a planar graph.
Briefly, the method is as follows. Let G be a directed graph with V (G)={v
Throughout this paper, we let G be a finite, connected graph with no loops or multiple edges. We denote the vertex set of G by V (G) and its edge set by E (G). A 1-factor of G is a set f of edges such that for every v E V (G) exactly one edge of f is incident on v. Kasteleyn [1] has introduced a technique for using Pfaffians to enumerate the 1-factors of a planar graph. Briefly, the method is as follows. Let G be a directed graph with V (G)={v
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