In a Steiner triple system of order v, STS(v), a set of three lines inter­ secting 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 ad­ missible 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( 6 n / 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 Av s , 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.
['Mike J. Grannell', 'T. S. Griggs', 'Roslyn Hill']
The triangle chromatic index of Steiner triple systems