Radon numbers and the fractional Helly theorem
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DOI: 10.1007/s11856-021-2102-8
Abstract: A basic measure of the combinatorial complexity of a convexity space is its Radon number. In this paper we answer a question of Kalai, by showing a fractional Helly theorem for convexity spaces with bounded… read more here.
Keywords: numbers fractional; helly theorem; radon numbers; convexity ... See more keywords
Quantitative Fractional Helly and (p,q)-Theorems
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DOI: 10.1016/j.ejc.2021.103424
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… read more here.
Keywords: helly theorems; fractional helly; quantitative fractional;