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 | |
| Publication status | Published - 2004 Aug 6 |
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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 journal › Article
}
TY - JOUR
T1 - Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces
AU - Nakamoto, Atsuhiro
AU - Negami, Seiya
AU - Ota, Katsuhiro
PY - 2004/8/6
Y1 - 2004/8/6
N2 - 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.
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.
KW - Chromatic number
KW - Cycle parity
KW - Quadrangulation
KW - Representativity
UR - http://www.scopus.com/inward/record.url?scp=3142533001&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3142533001&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2004.04.008
DO - 10.1016/j.disc.2004.04.008
M3 - Article
AN - SCOPUS:3142533001
VL - 285
SP - 211
EP - 218
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 1-3
ER -