MathDB

Let

P

be a set of

n

points and

S

a set of

l

segments. It is known that:

(i)

No four points of

P

are coplanar.

(ii)

Any segment from

S

has its endpoints at

P

(iii)

There is a point, say

g

, in

P

that is the endpoint of a maximal number of segments from

S

and that is not a vertex of a tetrahedron having all its edges in

S

. Prove that

l \leq \frac{n^2}{3}

Problem Statement