MathDB

Let

n

points

A_1, A_2, \ldots, A_n

, (

n>2

), be considered in the space, where no four points are coplanar. Each pair of points

A_i, A_j

are connected by an edge. Find the maximal value of

n

for which we can paint all edges by two colors – blue and red such that the following three conditions hold: I. Each edge is painted by exactly one color. II. For

i = 1, 2, \ldots, n

, the number of blue edges with one end

A_i

does not exceed 4. III. For every red edge

A_iA_j

, we can find at least one point

A_k

(

k \neq i, j

) such that the edges

A_iA_k

and

A_jA_k

are blue.

Problem Statement