On three parameters of invisibility graphs

  • Authors:

  • Josef Cibulka;Jan Kynčl;Viola Mészáros;Rudolf Stolař;Pavel Valtr

  • Affiliations:

  • Department of Applied Mathematics, Charles University, Faculty of Mathematics and Physics, Praha 1, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Faculty of Mathematics and Physics, Praha 1, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Faculty of Mathematics and Physics, Praha 1, Czech Republic and Bolyai Institute, University o ...;Department of Applied Mathematics, Charles University, Faculty of Mathematics and Physics, Praha 1, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Faculty of Mathematics and Physics, Praha 1, Czech Republic

  • Venue:
  • COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

The invisibility graph I(X) of a set X ⊆ Rd 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 Matouýek and Valtr claiming that for invisibility graphs of planar sets, the chromatic number cannot be bounded in terms of the clique number.