Quantitative Fractional Helly and (p,q)-Theorems

2020/12/16 by Jung, Attila, Naszódi, Márton · 1 citation
#52A35 #52A38 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2012.08964

Abstract

We consider quantitative versions of Helly-type questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main geometric result is a quantitative version of the Fractional Helly Theorem of Katchalski and Liu, the second one is a quantitative version of the (p,q)-Theorem of Alon and Kleitman.

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