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 |
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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