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

Multivariate Splines and the 4 Color Map Problem


This slide lists all the configurations making up an unavoidable set simply due to the observation that there must be a vertex of degree less than 6.

The vertex whose star we consider is marked green. Red edges may be shared with the rest of the triangulation. Thus the first three configurations are the stars of interior vertices of degree 3, 4, or 5. The remaining configurations may arise as the stars of boundary vertices of degree 2, 3, 4, or 5.

However, in the proof of the dimension statement for S14 we consider subtriangulation, and so the first three configurations in the second row may also arise as subtriangulations of the star of an interior vertex, part of which has already been removed.