Holes or Empty Pseudo-Triangles in Planar Point Sets

Abstract

Let E(k, ℓ) denote the smallest integer such that any set of at least E(k, ℓ) points in the plane, no three on a line, contains either an empty convex polygon with k vertices or an empty pseudo-triangle with ℓ vertices. The existence of E(k, ℓ) for positive integers k, ℓ ≥ 3, is the consequence of a result proved by Valtr [