Bounds on the achromatic number of partial triple systems
AbstractA 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.
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