Union-intersecting set systems
Combinatorics
2014-03-04 v1
Abstract
Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is l-intersecting. Then we investigate set systems where the union of any s sets intersect the union of any t sets. The maximal size of such a set system is determined exactly if s+t<5, and asymptotically if s+t>4. Finally, we exactly determine the maximal size of a k-uniform set system that has the above described (s,t)-union-intersecting property, for large enough n.
Cite
@article{arxiv.1403.0088,
title = {Union-intersecting set systems},
author = {Gyula O. H. Katona and Dániel T. Nagy},
journal= {arXiv preprint arXiv:1403.0088},
year = {2014}
}
Comments
9 pages