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

Multivariate Splines and the 4 Color Map Problem


Other topologies, for example of an 5-5 edge formation, are possible, but they would require the presence of vertices of degree 3 (Clough-Tocher vertices), which we have ruled out.

To make this unavoidable set complete we would have to edge formations where 1 or 2 of the vertices marked in blue are boundary vertices, and the subtriangulations of all these configurations.

Note: According to a private communication by Dan Sanders it is not necessary to include the configuration with vertices of degrees five and seven in the above unavoidable set.