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Radon numbers and the fractional Helly theorem

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arxiv 1903.01068 v1 pith:4BZW744F submitted 2019-03-04 math.CO

Andreas F. Holmsen , Dong-Gyu Lee This is my paper · ORCID
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keywords radonconvexitynumbertheoremboundedfractionalhellyquestion
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A basic measure of the combinatorial complexity of a convexity space is its Radon number. In this paper we show a fractional Helly theorem for convexity spaces with a bounded Radon number, answering a question of Kalai. As a consequence we also get a weak epsilon-net theorem for convexity spaces with a bounded Radon number. This answers a question of Bukh and extends a recent result of Moran and Yehudayoff.

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  1. Bounding Radon numbers via Betti numbers

    math.CO 2019-08 accept novelty 8.0 of 10

    Bounding low-degree Betti numbers of all intersections of a set family bounds its Radon number, giving an optimal surface fractional Helly theorem for b=0.

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