Combinatorial geometry of point sets with collinearities

Abstract

In this thesis various combinatorial problems relating to the geometry of point sets in the Euclidean plane are studied. The unifying theme is that all the problems involve point sets that are not in general position, but have some collinearities. Topics addressed include; Dirac's conjecture related to the maximum degree of visibility graphs, Erdős' general position subset selection problem, connectivity properties of visibility graphs, visibility in bichromatic point sets, and empty pentagons in point sets with collinearities.