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Total Z-transformation graphs of perfect matching of plane bipartite graphs

✍ Scribed by Heping Zhang; Fuji Zhang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
190 KB
Volume
5
Category
Article
ISSN
1571-0653

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Let G be a plane bipartite graph with at least two perfect matchings. The Z-transformation graph, ZF (G), of G with respect to a speciΓΏc set F of faces is deΓΏned as a graph on the perfect matchings of G such that two perfect matchings M1 and M2 are adjacent provided M1 and M2 di er only in a cycle t

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Let G be a plane bipartite graph which admits a perfect matching and with distinguished faces called holes. Let MG denote the perfect matchings graph: its vertices are the perfect matchings of G, two of them being joined by an edge, if and only if they di er only on an alternating cycle bounding a f

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Let G be a bipartite graph in which every edge belongs to some perfect matching, and let D be a subset of its edge set. It is shown that M fl D has the same parity for every perfect matching M if and only if D is a cut, and equivalently if and only. if (G, D) is a balanced signed-graph. This gives n