Summary: The maximum number of perfect matchings in graphs
with a given degree sequence
17 March, 2008
We show that the number of perfect matching in a simple graph G with an
even number of vertices and degree sequence d1, d2, . . . , dn is at most
This bound is sharp if and only if G is a union of complete balanced bipartite
2000 Mathematics Subject Classification: 05A15, 05C70.
Keywords and phrases: Perfect matchings, permanents.
Let G = (V, E) be an undirected simple graph. For a vertex v V , let deg v denote
its degree. Assume that |V | is even, and let perfmat G denote the number of perfect
matchings in G. The main result of this short note is: