A strong colouring of a hypergraph is an assignment of colours to its vertices so that no two vertices in a hyperedge have the same colour. We establish that strong colouring of partial triple systems is NP-complete, even when the number of colours is any fixed k≥3. In contrast, an efficient algorithm is given for strong colouring of maximal partial triple systems. Observations in this algorithm underpin a complete determination of the spectrum of strong chromatic numbers for maximal partial triple systems. © 1988.
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