Triangle-intersecting families on eight vertices

Abstract

Simonovits and Sós conjectured that the maximal size of a triangle-intersecting family of graphs on $n$ vertices is $2^{\left(\genfrac{}{}{0ex}{}{n}{2}\right)-3}$. Their conjecture has recently been proved using spectral methods. We provide an elementary proof of the special case of $8$ vertices using a partition argument.