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Grünbaum colorings of toroidal triangulations

✍ Scribed by Michael O. Albertson; Hannah Alpert; sarah-marie belcastro; Ruth Haas

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 140 KB
Volume: 63
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20406

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✦ Synopsis

Abstract

We prove that if G is a triangulation of the torus and χ(G)≠5, then there is a 3‐coloring of the edges of G so that the edges bounding every face are assigned three different colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 68–81, 2010

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## Abstract In 1976, Borodin conjectured that every planar graph has a 5‐coloring such that the union of every __k__ color classes with 1 ≤ __k__ ≤ 4 induces a (__k__—1)‐degenerate graph. We prove the existence of such a coloring using 18 colors. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:139