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
Clique number of Xor products of Kneser graphs
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 proposedExpand

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