# Two-Part Set Systems

@article{Erds2012TwoPartSS, title={Two-Part Set Systems}, author={P{\'e}ter L. Erd{\"o}s and D{\'a}niel Gerbner and Nathan Lemons and Dhruv Mubayi and Cory Palmer and Bal{\'a}zs Patk{\'o}s}, journal={Electron. J. Comb.}, year={2012}, volume={19}, pages={P52} }

The two part Sperner theorem of Katona and Kleitman states that if $X$ is an $n$-element set with partition $X_1 \cup X_2$, and $\mathcal{F}$ is a family of subsets of $X$ such that no two sets $A, B \in \mathcal{F}$ satisfy $A \subset B$ (or $B \subset A$) and $A \cap X_i=B\cap X_i$ for some $i$, then $|\mathcal{F}| \le {n \choose \lfloor n/2\rfloor}$. We consider variations of this problem by replacing the Sperner property with the intersection property and considering families that satisfy… Expand

#### One Citation

Clique number of Xor products of Kneser graphs

- Mathematics
- 2021

In this article we investigate a problem in graph theory, which has an equivalent reformulation in extremal set theory similar to the problems researched in [13] by Gyula O.H. Katona, who proposed… Expand

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