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 ε′≤n24=494.
Thus maximum ε′=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