Peter Alfeld, --- Department of Mathematics, --- College of Science --- University of Utah

Multivariate Splines and the 4 Color Map Problem


We can always add edges to a subtriangulation, and obtain a triangulation without adding vertices. The purpose of this process is to be able to utilize unavoidable sets defined for triangulations. Then the intersection of an unavoidable configuration of the extended triangulation with the present subtriangulation is an unavoidable configuration of the subtriangulation. It is not empty because every vertex of the triangulation is also a vertex of the subtriangulation.