VN-TST 1993 Problem 6

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.