Radon numbers and the fractional Helly theorem

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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 Radon number. As a consequence we also get a weak epsilon-net theorem for convexity spaces with bounded Radon number. This answers a question of Bukh and extends a recent result of Moran and Yehudayoff.
Publisher
Magnes Press
Issue Date
2021-03
Language
English
Article Type
Article
Citation

Israel Journal of Mathematics, v.241, no.1, pp.433 - 447

ISSN
0021-2172
DOI
10.1007/s11856-021-2102-8
URI
http://hdl.handle.net/10203/282414
Appears in Collection
MA-Journal Papers(저널논문)
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