# On 3-coloring of plane triangulations

Atsuhiro Nakamoto, Katsuhiro Ota, Mamoru Watanabe

### 抄録

Let G be a plane triangulation. For a 3-vertex-coloring λ, a face of G whose vertices receive all three colors is called a vivid face with respect to λ. Let hλ (G) be the number of vivid faces in G with respect to λ. Let C(G) be the set of 3-vertex-colorings of G and let g(n) be the set of plane triangulations with n faces. Let h(G) = max {hλ (G) {divides} λ ∈ C(G)} and h(n) = min {h(G) {divides} G ∈ g(n)}. In this paper we show that h(n) ≥ 1 2 n for any even n, and that h(n) ≤ 1 5 (3n - 2) for infinitely many n.

元の言語 English 519-524 6 Electronic Notes in Discrete Mathematics 11 https://doi.org/10.1016/S1571-0653(04)00097-6 Published - 2002 7

Triangulation
Coloring
Colouring
Face
Vertex Coloring
Divides
Color

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Applied Mathematics

### これを引用

On 3-coloring of plane triangulations. / Nakamoto, Atsuhiro; Ota, Katsuhiro; Watanabe, Mamoru.

：: Electronic Notes in Discrete Mathematics, 巻 11, 07.2002, p. 519-524.

Nakamoto, Atsuhiro ; Ota, Katsuhiro ; Watanabe, Mamoru. / On 3-coloring of plane triangulations. ：: Electronic Notes in Discrete Mathematics. 2002 ; 巻 11. pp. 519-524.
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