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 › peer-review

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

Keywords

Chromatic number
Cycle parity
Quadrangulation
Representativity

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2004.04.008

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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.",

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AU - Negami, Seiya

AU - Ota, Katsuhiro

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AB - 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.

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KW - Cycle parity

KW - Quadrangulation

KW - Representativity

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Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces

Abstract

Keywords

ASJC Scopus subject areas

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