Coloured matchings in bipartite graphs
โ Scribed by Kathie Cameron
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 213 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
A theorem of states that for every n x n (n ~> 3) complete bipartite graph G such that every edge is coloured and each colour is the colour of at most two edges, there is a perfect matching whose edges have distinct colours. We give an O(n 2) algorithm for finding such a perfect matching. We show that a related problem is NP-complete.
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.