On a conjecture of Karasev
Combinatorics
2018-05-15 v2 Metric Geometry
Abstract
Karasev conjectured that for any set of lines in general position in the plane, which is partitioned into color classes of equal size , the set can be partitioned into colorful 3-subsets such that all the triangles formed by the subsets have a point in common. Although the general conjecture is false, we show that Karasev's conjecture is true for lines in convex position. We also discuss possible generalizations of this result.
Cite
@article{arxiv.1712.00220,
title = {On a conjecture of Karasev},
author = {Seunghun Lee and Kangmin Yoo},
journal= {arXiv preprint arXiv:1712.00220},
year = {2018}
}