The extremal number of Venn diagrams
Combinatorics
2019-11-04 v1
Abstract
We show that there exists an absolute constant such that any family of size at least has dual VC-dimension at least 3. Equivalently, every family of size at least contains three sets such that all eight regions of their Venn diagram are non-empty. This improves upon the bound of Gupta, Lee and Li and is sharp up to the value of the constant.
Keywords
Cite
@article{arxiv.1911.00487,
title = {The extremal number of Venn diagrams},
author = {Peter Keevash and Imre Leader and Jason Long and Adam Zsolt Wagner},
journal= {arXiv preprint arXiv:1911.00487},
year = {2019}
}
Comments
11 pages