Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces

Atsuhiro Nakamoto, Seiya Negami, Katsuhiro Ota

Research output: Contribution to journalArticle

10 Citations (Scopus)

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)211-218
Number of pages8
JournalDiscrete Mathematics
Volume285
Issue number1-3
DOIs
Publication statusPublished - 2004 Aug 6

Fingerprint

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

Keywords

  • Chromatic number
  • Cycle parity
  • Quadrangulation
  • Representativity

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces. / Nakamoto, Atsuhiro; Negami, Seiya; Ota, Katsuhiro.

In: Discrete Mathematics, Vol. 285, No. 1-3, 06.08.2004, p. 211-218.

Research output: Contribution to journalArticle

Nakamoto, Atsuhiro ; Negami, Seiya ; Ota, Katsuhiro. / Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces. In: Discrete Mathematics. 2004 ; Vol. 285, No. 1-3. pp. 211-218.
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