Grünbaum colorings of triangulations on the projective plane

Michiko Kasai, Naoki Matsumoto, Atsuhiro Nakamoto

Abstract

A Grünbaum coloring of a triangulation G on a surface is a 3-edge coloring of G such that each face of G receives three distinct colors on its boundary edges. In this paper, we prove that every Fisk triangulation on the projective plane P has a Grünbaum coloring, where a “Fisk triangulation” is one with exactly two odd degree vertices such that the two odd vertices are adjacent. To prove the theorem, we establish a generating theorem for Fisk triangulations on P. Moreover, we show that a triangulation G on P has a Grünbaum coloring with each color-induced subgraph connected if and only if every vertex of G has even degree.

Original languageEnglish
Pages (from-to)155-163
Number of pages9
JournalDiscrete Applied Mathematics
Volume215
DOIs
StatePublished - 2016 Dec 31

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Triangulation
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Keywords

  • Grünbaum coloring
  • Projective plane
  • Triangulation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Grünbaum colorings of triangulations on the projective plane. / Kasai, Michiko; Matsumoto, Naoki; Nakamoto, Atsuhiro.

In: Discrete Applied Mathematics, Vol. 215, 31.12.2016, p. 155-163.

Research output: Contribution to journalArticle

Kasai, Michiko; Matsumoto, Naoki; Nakamoto, Atsuhiro / Grünbaum colorings of triangulations on the projective plane.

In: Discrete Applied Mathematics, Vol. 215, 31.12.2016, p. 155-163.

Research output: Contribution to journalArticle

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