Given is a surface represented through a triangle mesh (as commonly used in computer graphics, with vertices, edges and faces). The surface is known to be "watertight", i.e. no missing faces.
Is there a computationally efficient way to determine the genus (i.e. number of handles) of the surface represented by the mesh?
[I've tagged this as graph-theory because I believe this is a graph-theoretical problem, viewing the mesh as graph]