The Chromatic Number of the Convex Segment Disjointness Graph
نویسندگان
چکیده
Let P be a set of n points in general and convex position in the plane. Let Dn 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. [CGTA, 2005]. The previous best bounds are 3n 4 ≤ χ(Dn) < n − √ n 2 (ignoring lower order terms). In this paper we improve the lower bound to χ(Dn) ≥ n− √ 2n, to conclude a near-tight bound on χ(Dn).
منابع مشابه
The exact chromatic number of the convex segment disjointness graph
Let P be a set of n points in strictly convex position in the plane. Let Dn 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, Dumitrescu, Hurtado, Noy, and Urrutia [2005] and then by Dujmović and Wood [2007]. Improving on their estimates, we prove the following...
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