## Abstract This article shows that the vertices of a plane triangulation may be colored with 10 colors such that every pair of vertices has different colors if they are either adjacent or diagonal, that is, that they are not adjacent but are adjacent to two faces which share an edge. This improves
On 3-coloring of plane triangulations
โ Scribed by Atsuhiro Nakamoto; Katsuhiro Ota; Mamoru Watanabe
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 156 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
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## Abstract The vertices of each plane triangulation without loops and multiple edges may be colored with 11 colors so that for every two adjacent triangles [__xyz__] and [__wxy__], the vertices __x__,__y__,__w__,__z__ are colored pairwise differently.
## In the diagonal coloring of triangulations, not only adjacent vertices are colored differently but also any vertices z, w if there exist faces [xyz] and [WY]. An upper bound for the minimal number of colors needed to diagonally color any triangulation of a surface with Euler characteristic N is
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