Let $f(G)$ denote the number of $K_4$ in a graph $G$ and $e(G)$ denote the number of edges of $G$.

 

Consider two simple graphs $G_1$ and $G_2$ having the same set $V$ of $n$ vertices and let $H_1(U)$ and $H_2(U)$ be subgraphs of $G_1$ and $G_2$, respectively, having the same set $U$ of vertices.

 

If $M= {\max } |e(H_{1}(U))-e(H_{2}(U))|$, over all ${U \subseteq V, H_1 \subseteq G_1, H_2 \subseteq G_2}$, is it true that:

 

$|f(G_{1})-f(G_{2})| \leq Mn^2$?

I am looking for a proof or reference for the previous problem. Any suggestion would be appreciated.
Thanks in advance.

Let $f(G)$ denote the number of $K_4$ in a graph $G$ and $e(G)$ denote the number of edges of $G$.

Consider two simple graphs $G_1$ and $G_2$ having the same set $V$ of $n$ vertices and let $H_1(U)$ and $H_2(U)$ be subgraphs of $G_1$ and $G_2$, respectively, having the same set $U$ of vertices.

If $M= {\max } |e(H_{1}(U))-e(H_{2}(U))|$, over all ${U \subseteq V, H_1 \subseteq G_1, H_2 \subseteq G_2}$, is it true that:

$|f(G_{1})-f(G_{2})| \leq Mn^2$?

I am looking for a proof or reference for the previous problem. Any suggestion would be appreciated.
Thanks in advance.