# Three-line chromatic indices of Steiner triple systems

Grannell, M. J.; Griggs, T. S. and Rosa, A. (2000). Three-line chromatic indices of Steiner triple systems. Australasian Journal of Combinatorics, 21, pp. 67–84.

## Abstract

There are five possible structures for a set of three lines of a Steiner triple system. Each of these three-line configurations'' gives rise to a colouring problem in which a partition of all the lines of an STS() is sought, the components of the partition each having the property of not containing any copy of the configuration in question. For a three-line configuration , and STS() , the minimum number of classes required is denoted by and is called the -chromatic index of . This generalises the ordinary chromatic index and the 2-parallel chromatic index . (For the latter see .) In this paper we obtain results concerning for four of the five three-line configurations . In three of the cases we give precise values for all sufficiently large and in the fourth case we give an asymptotic result. The values of the four chromatic indices for are also determined.