Discrete & Computational Geometry

, Volume 11, Issue 2, pp 235–239 | Cite as

Unit squares intersecting all secants of a square

  • Pavel Valtr


LetS be a square of side lengths>0. We construct, for any sufficiently larges, a set of less than 1.994s closed unit squares whose sides are parallel to those ofS such that any straight line intersectingS intersects at least one square ofS. It disproves L. Fejes Tóth's conjecture that, for integrals, there is no such configuration of less than 2s−1 unit squares.


Line Segment Side Length Discrete Comput Geom Line intersectingS Vertical Line Segment 
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Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • Pavel Valtr
    • 1
    • 2
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic
  2. 2.Graduiertenkolleg “Algorithmische Diskrete Mathematik”, Fachbereich MathematikFreie Universität BerlinBerlin 33Germany

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