Let $G$ be a connected graph on 43 vertices. If $G$ does not contain an induced subgraph $K_{5}$, determine the maximum number of edges $G$ can have, and explain what $G$ looks like. You do not have to prove your choice of $G$ has maximum size.
I'm really not so sure how to approach this problem. It's a practice problem for an exam I'm preparing for. I tried it for smaller cases. For $n = 5$, we can have $9$ edges (just take $K_{5}$ and remove one edge). I think that we want to repeat this structure for $43$, so any $5$ vertices from our set of $43$ should have $9$ vertices?
I'm really not so sure. I would appreciate some help.
you can find that number using Turán's theorem. here: https://en.wikipedia.org/wiki/Tur%C3%A1n%27s_theorem