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.
Colbourn, C. J., Jungnickel, D., & Rosa, A. (1988). The strong chromatic number of partial triple systems. Discrete Applied Mathematics, 20(1), 31–38. https://doi.org/10.1016/0166-218X(88)90039-X