On the Number of Perfect Matchings in a Bipartite Graph
In this paper we show that, with 11 exceptions, any matching covered bipartite graph on $n$ vertices, with minimum degree greater than two, has at least $2n-4$ perfect matchings. Using this bound, which is the best possible, and McCuaig's theorem [W. McCuaig, J. Graph Theory, 38 (2001), pp. 124...
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| Veröffentlicht in: | SIAM journal on discrete mathematics 2013-01, Vol.27 (2), p.940-958 |
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| container_title | SIAM journal on discrete mathematics |
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| creator | de Carvalho, Marcelo H. Lucchesi, Cláudio L. Murty, U. S. R. |
| description | In this paper we show that, with 11 exceptions, any matching covered bipartite graph on $n$ vertices, with minimum degree greater than two, has at least $2n-4$ perfect matchings. Using this bound, which is the best possible, and McCuaig's theorem [W. McCuaig, J. Graph Theory, 38 (2001), pp. 124--169] on brace generation, we show that any brace on $n$ vertices has at least $(n-2)^2/8$ perfect matchings. A bi-wheel on $n$ vertices has $(n-2)^2/4$ perfect matchings. We conjecture that there exists an integer $N$ such that every brace on $n\geq N$ vertices has at least $(n-2)^2/4$ perfect matchings. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/120865938 |
| format | Article |
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| ispartof | SIAM journal on discrete mathematics, 2013-01, Vol.27 (2), p.940-958 |
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| language | eng |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Covering Graph theory Graphs Integers Matching Mathematical analysis Theorems |
| title | On the Number of Perfect Matchings in a Bipartite Graph |
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