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  • 1 Charles University Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI) Malostranské nám. 25 118 00 Praha 1 Czech Republic
  • 2 Eötvös University Institute of Mathematics Pázmány Péter sétány 1/C H-1117 Budapest Hungary
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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.