Bounds on the achromatic number of partial triple systems
DOI:
https://doi.org/10.11575/cdm.v2i1.61930Abstract
A complete kk-colouring of a hypergraph is an assignment of kk 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 kk such that it admits a complete kk-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.Downloads
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