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
Perfect matchings and ears in elementary bipartite graphs
β Scribed by Pierre Hansen; Fuji Zhang; Maolin Zheng
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 386 KB
- Volume
- 176
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We give lower and upper bounds for the number of reducible ears as well as upper bounds for the number of perfect matchings in an elementary bipartite graph. An application to chemical graphs is also discussed. In addition, a method to construct all minimal elementary bipartite graphs is described.
π SIMILAR VOLUMES
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
In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane