I'm currently working on a problem from Bondy & Murty. The question is below.
Show if the number of edges $m > \frac{1} {4}n (\sqrt{4n-3} + 1)$, $G$ contains a quadrilateral.
I know that I need to use that if $\sum \limits_v {d(v) \choose 2} > {n \choose 2}$ then the graph contains a quadrilateral, but it also says to use the Cauchy-Schwarz Inequality and I'm not sure which form that means (especially in terms of a graph). Any explanation of that would be much appreciated.
I'm not sure where to start, but I feel like that interpretation of the Cauchy-Schwarz Inequality will help me get an idea.