USAMO 1995 Problem 5

A graph with $\mathrm{n}$ points and $\mathrm{k}$ edges has no triangles. Show that it has a point $\mathrm{P}$ such that there are at most $\mathrm{k}(1$ $-4 k / \mathrm{n}^{2}$ ) edges between points not joined to P (by an edge).