Counting perfect matchings in n-extendable graphs

The structural theory of matchings is used to establish lower bounds on the number of perfect matchings in n-extendable graphs. It is shown that any such graph on p vertices and q   edges contains at least ⌈(n+1)!/4[q-p-(n-1)(2Δ-3)+4]⌉⌈(n+1)!/4[q-p-(n-1)(2Δ-3)+4]⌉ different perfect matchings, where ΔΔ is the maximum degree of a vertex in G.