Perfect matchings in regular bipartite graphs
โ Scribed by P. Katerinis; N. Tsikopoulos
- Publisher
- Springer Japan
- Year
- 1996
- Tongue
- English
- Weight
- 356 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
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
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.
Given a graph G and a subgraph H of G, let rb(G, H) be the minimum number r for which any edge-coloring of G with r colors has a rainbow subgraph H. The number rb(G, H) is called the rainbow number of H with respect to G. Denote as mK 2 a matching of size m and as B n,k the set of all the k-regular