Finite k-Transversals of Infinite Families of Fat Convex Sets

2022/12/28 by Chakraborty, Sutanoya, Ghosh, Arijit, Nandi, Soumi · 1 citation
#52A35 #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #G.2.m

paper · doi:10.48550/arxiv.2212.14091

Abstract

We prove an infinite (p,q)-theorem for piercing fat compact convex sets in \RR^d with k-flats. Additionally, we develop a new framework through which infinite (p,q)-theorems concerning compact sets and k-flats can be extended to their 'colorful' variants. Further, we show that the existence of an infinite (p,q)-theorem does not necessarily imply the existence of the corresponding finite (p,q)-theorem.

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• No Infinite (p,q)-Theorem for Piercing Compact Convex Sets with Lines in ℝ³

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