The chromatic number of the convex segment disjointness graph

Details The chromatic number of the convex segment disjointness graph The chromatic number of the convex segment disjointness graph

2011-05-25

arxiv.org/abs/1105.4931v2

Mathematics

Combinatorics

XIV Spanish Meeting on Computational Geometry Alcal\'a de Henares, Spain, June 27--30, 2011

Scientific paper

Let $P$ be a set of $n$ points in general and convex position in the plane. Let $D_n$ be the graph whose vertex set is the set of all line segments with endpoints in $P$, where disjoint segments are adjacent. The chromatic number of this graph was first studied by Araujo et al. [\emph{CGTA}, 2005]. The previous best bounds are $\frac{3n}{4}\leq\chi(D_n)

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