Periodica Mathematica Hungarica

, Volume 55, Issue 2, pp 121–127 | Cite as

Empty convex polygons in almost convex sets



A finite set of points, in general position in the plane, is almost convex if every triple determines a triangle with at most one point in its interior. For every ℓ ≥ 3, we determine the maximum size of an almost convex set that does not contain the vertex set of an empty convex ℓ-gon.

Key words and phrases

point configurations combinatorial convexity Erdős-Szekeres problem empty polygons 

Mathematics subject classification number



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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI)Charles UniversityPraha 1Czech Republic
  2. 2.Institute of MathematicsEötvös UniversityBudapestHungary

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