Graphs that triangulate a given surface and quadrangulate another surface

摘要

We show that for any closed surface F with chi(F) <= -4 (or chi(F) <= -2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadrangulate F. We also give a sufficient condition for a graph triangulating a closed surface to quadrangulate some other surface. (c) 2006 Elsevier Inc. All rights reserved.