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

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

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