Radon numbers and the fractional Helly theorem
Combinatorics
2019-03-05 v1
Abstract
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.
Cite
@article{arxiv.1903.01068,
title = {Radon numbers and the fractional Helly theorem},
author = {Andreas F. Holmsen and Dong-Gyu Lee},
journal= {arXiv preprint arXiv:1903.01068},
year = {2019}
}