Independent sets in Steiner triple systems

Forbes, A.D.; Grannell, M.J. and Griggs, T.S. (2004). Independent sets in Steiner triple systems. Ars Combinatoria, 72 pp. 161–169.

Abstract

A set of points in a Steiner triple system $({\rm STS}(v))$ is said to be independent if no three of these points occur in the same block. In this paper we derive for each $k\le8$ a closed formula for the number of independent sets of cardinality $k$ in an ${\rm STS}(v)$ . We use the formula to prove that every STS(21) has an independent set of cardinality eight and is as a consequence 4-colourable.