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 |
Keywords
- Chromatic number
- Cycle parity
- Quadrangulation
- Representativity
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
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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