The triangle chromatic index of Steiner triple systems

In a Steiner triple system of order v, STS(v), a set of three lines intersecting pairwise in three distinct points is called a triangle. A set of lines containing no triangle is called triangle-free. The minimum number of triangle-free sets required to partition the lines of a Steiner triple system S, is called the triangle chromatic index of S. We prove that for all admissible v, there exists an STS(v) with triangle chromatic index at most 8V3v. In addition, by showing that the projective geometry PG( n, 3) may be partitioned into O( 6n / 5) caps, we prove that the STS( v) formed from the points and lines of the affine geometry AG(n, 3) has triangle chromatic index at most Avs, where s = loge 6/(3 loge 5) ~ 0.326186, and A is a constant. We also determine the values of the index for STS( v) with v ::; 13.