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
✦ LIBER ✦
On the Number of Perfect Matchings in a Bipartite Graph
✍ Scribed by de Carvalho, Marcelo H.; Lucchesi, Cláudio L.; Murty, U. S. R.
- Book ID
- 120268386
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2013
- Tongue
- English
- Weight
- 471 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0895-4801
No coin nor oath required. For personal study only.
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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