Daniel McGinnis
Published 2020-10-25Version 1
We prove that every finite family of convex sets in the plane satisfying the $(4,3)$-property can be pierced by $9$ points. This improves the bound of $13$ proved by Gy\'arf\'as, Kleitman, and T\'oth in 2001.
Comments: The author was supported by NSF grant DMS-1839918 (RTG)
Pattern Recognition on Oriented Matroids: Halfspaces, Convex Sets and Tope Committees
On convex sets associated with permutations, cuts, and certain metrics
Piercing families of convex sets in the plane that avoid a certain subfamily with lines
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