Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces

Atsuhiro Nakamoto, Seiya Negami, Katsuhiro Ota

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10 Citations (Scopus)


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
Issue number1-3
Publication statusPublished - 2004 Aug 6



  • Chromatic number
  • Cycle parity
  • Quadrangulation
  • Representativity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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