# Largest number of perfect matchings in bounded genus graphs

What is the largest number of perfect matchings a genus $g$ bipartite graph on $n+m$ vertices have?

• Have you tried working out the values for some small values of n or m? – Yemon Choi May 1 '16 at 0:40
• $g$ scales with $n$ it is unlikely you get a nice formula so easily – T.... May 1 '16 at 0:42