  We give an upper bound on the number of perfect matchings in an undirected
simple graph $G$ with an even number of vertices, in terms of the degrees of
all the vertices in $G$. This bound is sharp if $G$ is a union of complete
bipartite graphs. This bound is a generalization of the upper bound on the
number of perfect matchings in bipartite graphs on $n+n$ vertices given by the
Bregman-Minc inequality for the permanents of $(0,1)$ matrices.
