New Conjectures for Union-Closed Families

@article{Pulaj2016NewCF,
  title={New Conjectures for Union-Closed Families},
  author={Jonad Pulaj and Annie Raymond and Dirk Oliver Theis},
  journal={Electron. J. Comb.},
  year={2016},
  volume={23},
  pages={P3.23}
}
The Frankl conjecture, also known as the union-closed sets conjecture, states that in any finite non-empty union-closed family, there exists an element in at least half of the sets. From an optimization point of view, one could instead prove that $2a$ is an upper bound to the number of sets in a union-closed family on a ground set of $n$ elements where each element is in at most $a$ sets for all $a,n\in \mathbb{N}^+$. Similarly, one could prove that the minimum number of sets containing the… Expand

Paper Mentions

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  • Jonad Pulaj
  • Mathematics, Computer Science
  • Math. Comput.
  • 2020
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