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Radon numbers and the fractional Helly theorem
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2021-02-16 , DOI: 10.1007/s11856-021-2102-8
Andreas F. Holmsen , Donggyu Lee

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 ε-net theorem for convexity spaces with bounded Radon number. This answers a question of Bukh and extends a recent result of Moran and Yehudayoff.



中文翻译:

数和分数阶Helly定理

凸空间的组合复杂度的基本度量是其Radon数。在本文中,我们通过显示有界Radon数的凸空间的分数阶Helly定理,回答了Kalai的问题。结果,对于有界Radon数的凸空间,我们也得到了一个弱ε- net定理。这回答了Bukh的问题,并扩展了Moran和Yehudayoff的最新结果。

更新日期:2021-02-16
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