Gr\"unbaum Colorings of Toroidal Triangulations
Michael O. Albertson, Hannah Alpert, sarah-marie belcastro, and Ruth, Haas

TL;DR
This paper proves that for any triangulation of the torus with chromatic number not equal to 5, a 3-edge-coloring exists where each face's boundary edges are all differently colored.
Contribution
It establishes a new coloring property for toroidal triangulations, extending understanding of face-edge colorings in topological graph theory.
Findings
Triangulations of the torus with chromatic number not 5 admit a 3-edge-coloring.
The result applies to all such triangulations, regardless of their specific structure.
Provides a new characterization of face-edge colorings in toroidal graphs.
Abstract
We prove that if G is a triangulation of the torus and \chi(G) \neq 5, then there is a 3-coloring of the edges of G so that the edges bounding every face are assigned three different colors.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Leaf Properties and Growth Measurement
