Bounds on the achromatic number of partial triple systems

Authors

  • Peter James Dukes
  • Gary MacGillivray
  • Kristin Parton

DOI:

https://doi.org/10.11575/cdm.v2i1.61930

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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Published

2007-03-08

Issue

Section

Articles