Improved Lower Bound for Frankl’s Union-Closed Sets Conjecture
We verify an explicit inequality conjectured in [Gilmer, 2022, arXiv:2211.09055], thus proving that for any nonempty union-closed family $\mathcal{F} \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $\mathcal{F} \$. One case, an explicit one-variable inequality, is checked by computer calculation.
Authors
- Mark Sellke (ORCID: https://orcid.org/0000-0001-9166-8185)
- Brice Huang (ORCID: https://orcid.org/0000-0001-5435-9754)
- Ryan Alweiss (ORCID: https://orcid.org/0000-0002-7221-4599)
Institutions
- University of Cambridge (GB)
- Moscow Institute of Thermal Technology (RU)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2024-09-20
- DOI
- https://doi.org/10.37236/12232
- Citations
- 1
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 1.32