Finding a maximum-genus graph imbedding
Merrick L. Furst, Jonathan L. Gross, Lyle A. McGeoch · Journal of the ACM · 1988
The computational complexity of constructing the imbeddings of a given graph into surfaces of different genus is not well understood. In this paper, topological methods and a reduction to linear matroid parity are used to develop a polynomial-time algorithm to find a maximum-genus cellular imbedding. This seems to be the first imbedding algorithm for which the running time is not exponential in the genus of the imbedding surface.