Bounds on the achromatic number of partial triple systems
Date
2007
Authors
Dukes, Peter J.
MacGillivray, Gary
Parton, Kristin
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Volume Title
Publisher
Contributions to Discrete Mathematics
Abstract
A 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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Citation
Dukes, 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.v2i1.61930