On 3-coloring of plane triangulations

Atsuhiro Nakamoto, Katsuhiro Ota, Mamoru Watanabe

研究成果: Article査読

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.

本文言語English
ページ(範囲)519-524
ページ数6
ジャーナルElectronic Notes in Discrete Mathematics
11
DOI
出版ステータスPublished - 2002 7月 1

ASJC Scopus subject areas

  • 離散数学と組合せ数学
  • 応用数学

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