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{\bf Noga Alon and Shmuel Friedland}
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{\bf The Maximum Number of Perfect Matchings in Graphs with a Given Degree Sequence}
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We show that the number of perfect matchings in a simple graph
$G$ with an even number of vertices and degree sequence
$d_1,d_2, \ldots ,d_n$ is at most $ \prod_{i=1}^n (d_i!)^{{1\over 2d_i}}$.
This bound is sharp if and only if $G$ is a union of complete
balanced bipartite graphs.



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