On 3-coloring of plane triangulations

Atsuhiro Nakamoto, Katsuhiro Ota, Mamoru Watanabe

Research output: Contribution to journalArticle


For a 3-vertex coloring, a face of a triangulation whose vertices receive all three colors is called a vivid face with respect to it. In this paper, we show that for any triangulation G with n faces, there exists a coloring of G with at least 1/2n faces and construct an infinite series of plane triangulations such that any 3-coloring admits at most 1/5 (3n - 2) vivid faces.

Original languageEnglish
Pages (from-to)157-162
Number of pages6
JournalArs Combinatoria
Publication statusPublished - 2005 Apr 1



  • 3-coloring
  • Plane triangulation
  • Triangulation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nakamoto, A., Ota, K., & Watanabe, M. (2005). On 3-coloring of plane triangulations. Ars Combinatoria, 75, 157-162.