Strict colourings for classes of STS

We investigate the largest number of colours, called upper chromatic number and denoted \bar(\chi)(H), that can be assigned to the vertices (points) of a teiner triple system H in such a way that every block H is an element of H contains at least two vertices of the same colour. The exact value of \bar(\chi) is determined for some classes of triple systems, and it is observed further that optimal colourings with the same number of colours exist also under the additional assumption that no monochromatic block occurs. Examples show, however, that the cardinalities of the colour classes in the latter case are more strictly determined.