For a finite graph
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
, let
![f(G)](/media/m/2/7/d/27d7f717a8c7df1eb318ae2082d5982b.png)
be the number of triangles and
![g(G)](/media/m/c/f/5/cf5379749bc8a2096560da05f25c390a.png)
the number of tetrahedra formed by edges of
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
. Find the least constant
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
such that
![g(G)^3 \leq c\cdot f(G)^4](/media/m/4/3/b/43b899d8d97fc7044849806928b8bfae.png)
for every graph
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
.
%V0
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
$g(G)^3 \leq c\cdot f(G)^4$
for every graph $G$.