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A Distributive Lattice on the Set of Perfect Matchings of a Plane Bipartite Graph

✍ Scribed by Peter Che Bor Lam; Heping Zhang


Book ID
111542615
Publisher
Springer Netherlands
Year
2003
Tongue
English
Weight
176 KB
Volume
20
Category
Article
ISSN
0167-8094

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Let G be a bipartite graph with 2n vertices, A its adjacency matrix and K the number of perfect matchings. For plane bipartite graphs each interior face of which is surrounded by a circuit of length 4s + 2, s E { 1,2,. . .}, an elegant formula, i.e. det A = (-1 )nK2, had been rigorously proved by Cv