Let $G = (V(G),E(G))$ be a singular graph with $n=10$ and $|E|= 28$. Show that $G$ contains a cycle of length $4$.
The question says it all. Our teacher gave us the hint that it is similar to another question that we answered using combinatorics and double counting techniques with properties of singular graphs. (in that case: we had G' = (V(G),E(G)) singular, with $n=10$ and $|E|=38$, show that $G$ contains $K_{4}$.)
But I don't know how to solve this one, I don't know how to start with this proof. What is the best way? Constructive proof where we draw the graph and show that we avoid having a cycle of length $4$ and that eventually, you have to have a connection which gives length $4$ or is this solveable in other ways?