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The Chromatic Number of the Convex Segment Disjointness Graph

  • Ruy Fabila-Monroy
  • David R. Wood
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

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 ).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ruy Fabila-Monroy
    • 1
  • David R. Wood
    • 2
  1. 1.Departamento de MatemáticasCentro de Investigación y Estudios Avanzados del Instituto Politécnico NacionalMéxico, D.F.México
  2. 2.Department of Mathematics and StatisticsThe Univesity of MelbourneMelbourneAustralia

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