Question 15
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
$$ g(G)^{3}\leq c\cdot f(G)^{4}{\mathrm{~f o r~e v e r y~g r a p h~}}G. $$
$$ g(G)^{3}\leq c\cdot f(G)^{4}{\mathrm{~f o r~e v e r y~g r a p h~}}G. $$