Can anyone please help me with this question? How can i start it?
Show that if G is a bipartite simple graph with v vertices and e edges, then e ≤ v²/4
let $\displaystyle V$ be the set of vertices. then $\displaystyle V=A \cup B,$ where $\displaystyle A \cap B= \emptyset, \ |A|=m, \ |B|=n.$ clearly $\displaystyle v=m+n$ and $\displaystyle e \leq mn.$ we also have $\displaystyle mn \leq \frac{(m+n)^2}{4}$ because $\displaystyle (m-n)^2 \geq 0.$