The maximum number of perfect matchings in graphs with a given degree sequence
Summary: We show that the number of perfect matchings in a simple graph \(G\) with an even number of vertices and degree sequence \(d_1,d_2, \dots ,d_n\) is at most \(\pi_{i=1}^n (d_i!)^{\frac{1}{2d_i}}\). This bound is sharp if and only if \(G\) is a union of complete balanced bipartite graphs.
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