Chromatic Numbers and Cycle Parities of Quadrangulations on Nonorientable Closed Surfaces

Atsuhiro Nakamoto, Seiya Negami, Katsuhiro Ota

Research output: Contribution to journalArticle

Abstract

In this paper, we shall show that every quadrangulation on a nonorientable closed surface with sufficiently large representativity has chromatic number 2, 3 or 4 and characterize those for each value, discussing an algebraic invariant called a cycle parity. In particular, we shall prove that such a quadrangulation is 4-chromatic if and only if it has an odd cycle which cuts open the host surface into an orientable surface.

Original languageEnglish
Pages (from-to)509-518
Number of pages10
JournalElectronic Notes in Discrete Mathematics
Volume11
DOIs
Publication statusPublished - 2002 Jul

Fingerprint

Quadrangulation
Chromatic number
Parity
Cycle
Closed
Odd Cycle
If and only if
Invariant

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Chromatic Numbers and Cycle Parities of Quadrangulations on Nonorientable Closed Surfaces. / Nakamoto, Atsuhiro; Negami, Seiya; Ota, Katsuhiro.

In: Electronic Notes in Discrete Mathematics, Vol. 11, 07.2002, p. 509-518.

Research output: Contribution to journalArticle

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