Unique Embeddings for Graphs on Orientable Surfaces Permitting Short Noncontractible Cycles
Yanpei Liu · Journal of Mathematical Research and Exposition · 2004
A fundamental result in topological graph theory by H.Whitney states that a 3-connected graph has at most one planar embedding. C.Thomassen generalized this to LEW-embeddings on higher surfaces. We establish several unique embedding results for 3-connected graphs on orientable surfaces which admit relatively large facial walks and rcpresentativity and hence generalize Thomassen's uniqueness theorem on LEW-embeddings.