On 3-coloring of plane triangulations

Atsuhiro Nakamoto, Katsuhiro Ota, Mamoru Watanabe

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)519-524
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume11
DOIs
Publication statusPublished - 2002 Jul

Fingerprint

Triangulation
Coloring
Colouring
Face
Vertex Coloring
Divides
Color

Keywords

  • 3-coloring
  • plane triangulation
  • triangulation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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

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

Research output: Contribution to journalArticle

Nakamoto, Atsuhiro ; Ota, Katsuhiro ; Watanabe, Mamoru. / On 3-coloring of plane triangulations. In: Electronic Notes in Discrete Mathematics. 2002 ; Vol. 11. pp. 519-524.
@article{e45e095b75cc4283afcbb388d9481055,
title = "On 3-coloring of plane triangulations",
abstract = "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.",
keywords = "3-coloring, plane triangulation, triangulation",
author = "Atsuhiro Nakamoto and Katsuhiro Ota and Mamoru Watanabe",
year = "2002",
month = "7",
doi = "10.1016/S1571-0653(04)00097-6",
language = "English",
volume = "11",
pages = "519--524",
journal = "Electronic Notes in Discrete Mathematics",
issn = "1571-0653",
publisher = "Elsevier",

}

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 -