Given seven points in the plane, some of them are connected by segments such that:
(i) among any three of the given points, two are connected by a segment;
(ii) the number of segments is minimal.
How many segments does a figure satisfying (i) and (ii) have? Give an example of such a figure.
Again Turan, in $G'$ we have no triangle by (i), so we have $\varepsilon '\leq {n^2\over 4} = {49\over 4}$.
Thus maximum $\varepsilon' = 12$ so minimum $\varepsilon = {7\choose 2}-12 = 9$.
Now minimal configuration is union $K_3$ and $K_4$.
$4G \le\ n^2$ by the well known mantels theorem
So here n=7 actually you we are to consider [n^2/4] so that n=7
So min is 12 and for minimum 7C2–12
There is nothing so difficult