The Union-Closed Sets Conjecture for Small Families

Abstract

We prove that the union-closed sets conjecture is true for separating union-closed families $\mathcal{A}$ with $|\mathcal{A}|\le 2\left(m+\frac{m}{{\log }_2(m)-{\log }_2{\log }_2(m)}\right)$ where $m$ denotes the number of elements in $\mathcal{A}$.

5 pages

References in corpus (1)

• Graph generated union-closed families of sets