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On Three Parameters of Invisibility Graphs

  • Josef Cibulka
  • Jan Kynčl
  • Viola Mészáros
  • Rudolf Stolař
  • Pavel Valtr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6196)

Abstract

The invisibility graph I(X) of a set \(X \subseteq {\mathbb R}^d\) is a (possibly infinite) graph whose vertices are the points of X and two vertices are connected by an edge if and only if the straight-line segment connecting the two corresponding points is not fully contained in X.

We settle a conjecture of Matoušek and Valtr claiming that for invisibility graphs of planar sets, the chromatic number cannot be bounded in terms of the clique number.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Josef Cibulka
    • 1
  • Jan Kynčl
    • 2
  • Viola Mészáros
    • 2
    • 3
  • Rudolf Stolař
    • 1
  • Pavel Valtr
    • 2
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic
  2. 2.Department of Applied Mathematics and, Institute for Theoretical Computer Science, Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic
  3. 3.Bolyai InstituteUniversity of SzegedSzegedHungary

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