An Attempt at Frankl's Conjecture


Petar Marković


In 1979 Frankl conjectured that in a finite union-closed family $\F$ of finite sets, $\F\neq\{\emptyset\}$ there has to be an element that belongs to at least half of the sets in $\F$. We prove this when $|\bigcup{\mathcal F}|\leq 10$.