Finding the topological genus of a triangulated surface 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]

$2-2g=$ number of vertices - number of edges + number of faces ($g$ is the genus and $2-2g$ is the Euler characteristic). In your case number of edges = $3/2$ times number of faces (triangles).