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 1

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Chromatic Numbers and Cycle Parities of Quadrangulations on Nonorientable Closed Surfaces'. Together they form a unique fingerprint.

  • Cite this