Graphs that triangulate a given surface and quadrangulate another surface

We show that for any closed surface F with χ(F) −4 (or χ(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. © 2006 Elsevier Inc. All rights reserved.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Yusuke Suzuki
• Keywords: Closed Surface, JCT 2006, JCT 2007, Klein Bottle, Projective Plane