For any graph $G$ on $n$ vertices, not containing a $4$-cycle, prove that $$E(G)\le{n\over 4}\left(1+\sqrt{4n-3}\right)$$
Can someone tell me how to even approach?Not containing a 4-cycle means it can contain both $3$ cycles and $5$ cycles , right? How to handle such stuff in Ramsey Theory? An answer will be appreciated..