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On Three Parameters of Invisibility Graphs

  • Conference paper
Computing and Combinatorics (COCOON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

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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.

Work on this paper was supported by the project 1M0545 of the Ministry of Education of the Czech Republic. The third author was also supported by OTKA Grant K76099 and by the grant no. MSM0021620838 of the Ministry of Education of the Czech Republic. The first and fourth authors were also supported by the Czech Science Foundation under the contract no. 201/09/H057. The first, second and fifth authors were partially supported by project GAUK 52110.

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References

  1. Breen, M., Kay, D.C.: General decomposition theorems for m-convex sets in the plane. Israel Journal of Mathematics 24, 217–233 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Erdős, P., Szekeres, G.: A combinatorial problem in geometry. Compos. Math. 2, 463–470 (1935)

    Google Scholar 

  3. Hell, P., Nešetřil, J.: Graphs and Homomorphisms. Oxford University Press, Oxford (2004)

    Book  MATH  Google Scholar 

  4. Matoušek, J.: Lectures on Discrete Geometry. Springer, New York (2002)

    MATH  Google Scholar 

  5. Matoušek, J., Valtr, P.: On visibility and covering by convex sets. Israel Journal of Mathematics 113, 341–379 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Perles, M., Shelah, S.: A closed (n + 1)-convex set in ℝ2 is a union of n 6 convex sets. Israel Journal of Mathematics 70, 305–312 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Josef Cibulka & Rudolf Stolař

  2. Department of Applied Mathematics and, Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jan Kynčl, Viola Mészáros & Pavel Valtr

  3. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary

    Viola Mészáros

Authors
  1. Josef Cibulka
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  2. Jan Kynčl
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  3. Viola Mészáros
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  4. Rudolf Stolař
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  5. Pavel Valtr
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Editor information

Editors and Affiliations

  1. University of Florida, CSE Building, Room 566, P.O. Box 116120, 32611-6120, Gainesville, Florida, USA

    My T. Thai

  2. Department of Computer and Information Science and Technology, University of Florida, P.O. Box, USA

    Sartaj Sahni

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© 2010 Springer-Verlag Berlin Heidelberg

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Cibulka, J., Kynčl, J., Mészáros, V., Stolař, R., Valtr, P. (2010). On Three Parameters of Invisibility Graphs. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_22

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  • DOI: https://doi.org/10.1007/978-3-642-14031-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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