摘要：The genus of a graph is a basic parameter in topological graph theory that has been the subject of extensive study. Perhaps surprisingly, despite its importance, the problem of approximating the genus of a graph is very poorly understood. Thomassen (1989) showed that computing the exact genus is NP-complete, and the best known upper bound for general graphs is an O(n)O(n)-approximation that follows by Euler's characteristic.We give a polynomial-time pseudo-approximation algorithm for the orientable genus of Hamiltonian graphs. More specifically, on input a graph GG of orientable genus gg and a Hamiltonian path in GG, our algorithm computes a drawing on a surface of either orientable or non-orientable genus O(g7)O(g7).
