ISL 2004 C8

For a finite graph $G$ , let $f(G)$ be the number of triangles and $g(G)$ the number of tetrahedra formed by edges of $G$ . Find the least constant $c$ such that $$g(G)^3\le c\cdot f(G)^4$$ for every graph $G$ .

Proposed by Marcin Kuczma, Poland