2017/12/01 by Seunghun Lee, Lee, Seunghun, Kangmin Yoo +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG
paper · pdf · doi:10.48550/arxiv.1712.00220
arxiv created 2018/05/13 · arxiv updated 2018/05/15
Karasev conjectured that for any set of 3k lines in general position in the plane, which is partitioned into 3 color classes of equal size k, the set can be partitioned into k 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.