Publication at Faculty of Mathematics and Physics |
2009
Abstract
We prove that for any partition of the plane into a closed set C and an open set O and for any configuration T of three points, there is a translated and rotated copy of T contained in C or in O. We also show that for any polygonal partition and any configuration T which is a vertex set of a non-equilateral triangle there is a copy of T contained in the interior of one of the two partition classes.
Furthermore, we characterize the polygonal partitions that avoid copies of a given equilateral triple.