Abstract
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.
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Communicated by Imre Bárány
Research was supported by project LN00A056 of The Ministry of Education of the Czech Republic.
Partially supported by grants T043631 and NK67867 of the Hungarian NFSR (OTKA).
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Valtr, P., Lippner, G. & Károlyi, G. Empty convex polygons in almost convex sets. Period Math Hung 55, 121–127 (2007). https://doi.org/10.1007/s10998-007-4121-z
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DOI: https://doi.org/10.1007/s10998-007-4121-z