The maximum number of intersections of two polygons

Abstract

We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p and q are both odd and both polygons are simple, the problem is more difficult. The conjectured maximum is (p-1)(q-1)+2 for all odd p and q.

This paper has been withdrawn by the author due to an unrecoverable error in the proof of Lemma 2. In fact, a counterexample to an even weaker version of Lemma 2 has been found by the author

Cited by in corpus (1)

• An almost optimal bound on the number of intersections of two simple polygons