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 |
|---|---|
| ページ（範囲） | 519-524 |
| ページ数 | 6 |
| ジャーナル | Electronic Notes in Discrete Mathematics |
| 巻 | 11 |
| DOI | |
| 出版物ステータス | Published - 2002 7 |
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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.研究成果: Article
}
TY - JOUR
T1 - On 3-coloring of plane triangulations
AU - Nakamoto, Atsuhiro
AU - Ota, Katsuhiro
AU - Watanabe, Mamoru
PY - 2002/7
Y1 - 2002/7
N2 - 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.
AB - 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.
KW - 3-coloring
KW - plane triangulation
KW - triangulation
UR - http://www.scopus.com/inward/record.url?scp=34247178092&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34247178092&partnerID=8YFLogxK
U2 - 10.1016/S1571-0653(04)00097-6
DO - 10.1016/S1571-0653(04)00097-6
M3 - Article
AN - SCOPUS:34247178092
VL - 11
SP - 519
EP - 524
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
SN - 1571-0653
ER -