It was shown (Kronk and Mitchen, 1973) that the set of vertices, edges and faces of any normal map on the sphere can be colored with seven colors. In this paper we solve a somewhat different problem: the set of edges and faces of any plane graph with A ~< 3 can be colored by six colors.
A six-coloring of the plane
β Scribed by Alexander Soifer
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 103 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0097-3165
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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.
A sequence r 1 , r 2 , . . . , r 2n such that r i = r n+i for all 1 β€ i β€ n is called a repetition. A sequence S is called non-repetitive if no block (i.e. subsequence of consecutive terms of S) is a repetition. Let G be a graph whose edges are colored. A trail is called non-repetitive if the sequen