Dukes, Peter J.MacGillivray, GaryParton, Kristin2021-03-012021-03-0120072007Dukes, P. J., MacGillivray, G., & Parton, K. (2007). Bounds on the achromatic number of partial triple systems. Contributions to Discrete Mathematics, 2(1), 1-12. https://doi.org/10.11575/cdm.v2i1.61930https://doi.org/10.11575/cdm.v2i1.61930http://hdl.handle.net/1828/12742A complete k-colouring of a hypergraph is an assignment of k colours to the points such that (1) there is no monochromatic hyperedge, and (2) identifying any two colours produces a monochromatic hyperedge. The achromatic number of a hypergraph is the maximum k such that it admits a complete k-colouring. We determine the maximum possible achromatic number among all maximal partial triple systems, give bounds on the maximum and minimum achromatic numbers of Steiner triple systems, and present a possible connection between optimal complete colourings and projective dimension.enArticleDepartment of Mathematics and Statistics