Geodesic
The maximum number of perfect matchings in graphs with a given degree sequence
The electronic journal of combinatorics, Tome 15 (2008)
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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.
DOI : 10.37236/888
Classification : 05C70, 05A15, 05C07
Mots-clés : perfect matchings, permanents, complete balanced bipartite graphs 
@article{10_37236_888,
     author = {Noga Alon and Shmuel Friedland},
     title = {The maximum number of perfect matchings in graphs with a given degree sequence},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/888},
     zbl = {1183.05064},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/888/}
}
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Noga Alon; Shmuel Friedland. The maximum number of perfect matchings in graphs with a given degree sequence. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/888

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