Triangle-free graph with 5 vertices What is the maximum number of edges in a triangle-free graph on 5 vertices?
No answers, please...just hints.
I believe that E $\leq$ 5, but I'm not sure where to go from there.

Hint: a triangle free graph on $5$ vertices is bipartite unless it contains a $5$ cycle. But if it has a $5$ cycle and is triangle free it is a cycle.
Hence you want to find the bipartite graph with five vertices with the most edges.
