Chromatic numbers of the hyperbolic surfaces
| Autor: | Hugo Parlier, Camille Petit |
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| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Surface (mathematics) Mathematics::Combinatorics General Mathematics 010102 general mathematics Geometric Topology (math.GT) Space (mathematics) 01 natural sciences Combinatorics Mathematics - Geometric Topology Metric space Differential Geometry (math.DG) Computer Science::Discrete Mathematics Genus (mathematics) FOS: Mathematics Mathematics [G03] [Physical chemical mathematical & earth Sciences] Mathematics - Combinatorics Combinatorics (math.CO) Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] Chromatic scale 0101 mathematics Mathematics |
| Zdroj: | Indiana Univ. Math. Journal Indiana Univ. Math. J. |
| DOI: | 10.1512/iumj.2016.65.5842 |
| Popis: | This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the $d$-chromatic number is the minimum number of colors needed to color the points of the space so that any two points at distance $d$ are of a different color. We prove upper bounds on the $d$-chromatic number of any hyperbolic surface which only depend on $d$. In another direction, we investigate chromatic numbers of closed genus $g$ surfaces and find upper bounds that only depend on $g$ (and not on $d$). For both problems, we construct families of examples that show that our bounds are meaningful. 24 pages, 12 figures |
| Databáze: | OpenAIRE |
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