On the minimum order of a quadrangulation on a given closed 2-manifold
  A partial formula is provided to calculate the smallest number of vertices possible in a quadrangulation on the closed orientable 2-manifold of given genus. This extends the previously known partial formula due to N. Hartsfield and G. Ringel [J. Comb. Theory, Ser. B, 1989, 46, 84-95]. 
Serge Lawrencenko
math.CO cs.DM math.AT math.GT