Independent sets in Steiner triple systems

A set of points in a Steiner triple system (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 8 a closed formula for the number of independent sets of cardinality k in an 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. AMS classification: 05B07

• Type: Journal
• Year: 2004
• Where: ARSCOM
• Authors: A. D. Forbes, Mike J. Grannell, Terry S. Griggs
• Keywords: ARSCOM 2004, Closed Formula, Independent Set, Steiner Triple System