Discrete & Computational Geometry

, Volume 20, Issue 2, pp 179–187 | Cite as

On the independence number of minimum distance graphs

  • G. Csizmadia


Let F=F(n) denote the largest number such that any set of n points in the plane with minimum distance 1 has at least F elements, no two of which are at unit distance. Improving a result by Pollack, we show that F(n) ≥ 9/35n. We also give an O(n log n) time algorithm for selecting at least 9/35n elements in a set of n points with minimum distance 1 so that no two selected points are at distance 1.


Minimum Distance Discrete Comput Geom Common Neighbor Special Pair Independence Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    P. Erdős. Some combinatorial and metric problems in geometry, In: Intuitive Geometry, Colloquia Mathematica Societatis János Bolyai, vol. 48 (K. Böröczky and G. Fejes Tóth, Eds.), North-Holland, Amsterdam, pp. 167–177, 1985.Google Scholar
  2. 2.
    J. Pach and P. K. Agarwal. Combinatorial Geometry, Wiley, New York, 1995.zbMATHGoogle Scholar
  3. 3.
    J. Pach and G. Tóth. On the independence number of coin graphs, Geombinatorics 6(1), 30–33, 1996.zbMATHMathSciNetGoogle Scholar
  4. 4.
    R. Pollack. Increasing the minimum distance of a set of points, J. Combinatorial, Theory, Series A, 40, 450, 1985.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • G. Csizmadia
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

Personalised recommendations