A Note on Solid Coloring of Pure Simplicial Complexes

Details A Note on Solid Coloring of Pure Simplicial Complexes A Note on Solid Coloring of Pure Simplicial Complexes

2010-12-17

arxiv.org/abs/1012.4017v1

Computer Science

Discrete Mathematics

11 pages, 6 figures

Scientific paper

We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in R^d may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R^2 this says that any planar map all of whose faces are triangles may be 3-colored, and in R^3 it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.

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