Three-line chromatic indices of Steiner triple systems

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(v) 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 B, and STS (v) S, the minimum number of classes required is denoted by …