A note on the colorful fractional Helly theorem

Abstract

Helly's theorem is a classical result concerning the intersection patterns of convex sets in ${\mathbb{R}}^d$. Two important generalizations are the colorful version and the fractional version. Recently, Bárány et al. combined the two, obtaining a colorful fractional Helly theorem. In this paper, we give an improved version of their result.

Cited by in corpus (2)

• Nerves, minors, and piercing numbers
• Fractional Helly theorem for Cartesian products of convex sets