Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces

Atsuhiro Nakamoto; Seiya Negami; Katsuhiro Ota

doi:10.1016/j.disc.2004.04.008

Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces

Atsuhiro Nakamoto, Seiya Negami, Katsuhiro Ota

Department of Mathematics

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	211-218
Number of pages	8
Journal	Discrete Mathematics
Volume	285
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.04.008
Publication status	Published - 2004 Aug 6

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Keywords

Chromatic number
Cycle parity
Quadrangulation
Representativity

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Cite this

Nakamoto, A., Negami, S., & Ota, K. (2004). Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces. Discrete Mathematics, 285(1-3), 211-218. https://doi.org/10.1016/j.disc.2004.04.008

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Access to Document

10.1016/j.disc.2004.04.008