2021/12/07 by Ricardo Strausz, Strausz, Ricardo
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Computational Geometry and Mesh Generation #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2112.04908
The aim of this note is to give an elementary proof of the following fact: given 3 red convex sets and 3 blue convex sets in 𝔼3, such that every red intersects every blue, there is a line transversal to the reds or there is a line transversal to the blues. This is a special case of a theorem of Montajano and Karasev \citeMK and generalizes, in a sense, the colourful Helly theorem due to Lovász (cf. \citeBL).