Uniquely 3-colourable Steiner triple systems

  • Authors:

  • A. D. Forbes

  • Affiliations:

  • Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2003

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Abstract

A Steiner triple system (STS(υ)) is said to be 3-balanced if every 3-colouring of it is equitable; that is, if the cardinalities of the colour classes differ by at most one. A 3-colouring, φ, of an STS(υ) is unique if there is no other way of 3-colouring the STS(υ) except possibly by permuting the colours of φ. We show that for every admissible υ ≥ 25, there exists a 3-balanced STS(υ) with a unique 3-colouring and an STS(υ) which has a unique, non-equitable 3- colouring.