ON POINT SETS WITHOUT k COLLINEAR POINTS
Peter Braß · 2003
In the following we discuss two problems on sets of n points in the plane, in which no k points are collinear: • the maximum number of k — 1-point lines (generalized orchard problem), and • the largest cardinality of a subset with no k — 1 points collinear. For both problems we present a slight improvement of the current bounds. We also give a simpler construction that reaches the same asymptotic bounds as Ismailescu's recent construction, which in turn improved Grunbaum's long-standing lower bound.