Avoiding Repetitions on the Plane

Tuesday, March 31, 2015 - 2:00pm - 3:00pm
Lind 305
Barbara Pilat (Warsaw University of Technology)
Inspired by classical Hadwiger-Nelson problem on chromatic number of R^2, we want to determine the number of colors required to avoid repetitions
on R^2. Since it turns out that in the above problem we need infinitely
many colors, we relax the problem. Namely, we show that 53 colors is enough to
avoid repetitions on paths of collinear points. On the other hand, we show what can be avoided using only 2 colors. Joint work with M. Dębski, J. Grytczuk, U. Pastwa, J. Sokół, M. Tuczyński, P. Wenus, K. Węsek.