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Forbes, A.D.; Grannell, M.J. and Griggs, T.S.
(2003).
DOI: https://doi.org/10.1016/S0012-365X(02)00473-9
Abstract
A Steiner triple system, STS(v), is said to be χ-chromatic if the points can be coloured using χ colours, but no fewer, such that no block is monochromatic. All known 3-chromatic STS(v) are also equitably colourable, i.e. there exists a 3-colouring in which the cardinalities of the colour classes differ by at most one. We present examples of 3-chromatic STS(v) which do not admit equitable 3-colourings. We also present further examples of systems with unique and balanced colourings