Abstract
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. [CGTA, 2005]. The previous best bounds are \(\frac{3n}{4}\leq \chi(D_n) <n-\sqrt{\frac{n}{2}}\) (ignoring lower order terms). In this paper we improve the lower bound to \(\chi(D_n)\geq n-\sqrt{2n}\), achieving near-tight bounds on χ(D n ).
Dedicat al nostre amic i mestre Ferran Hurtado.
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Fabila-Monroy, R., Wood, D.R. (2012). The Chromatic Number of the Convex Segment Disjointness Graph. In: Márquez, A., Ramos, P., Urrutia, J. (eds) Computational Geometry. EGC 2011. Lecture Notes in Computer Science, vol 7579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34191-5_7
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DOI: https://doi.org/10.1007/978-3-642-34191-5_7
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