Star chromatic numbers of hypergraphs and partial Steiner triple systems

The concept of star chromatic number of a graph, introduced by Vince (1988) is a natural generalization of the chromatic number of a graph. This concept was studied from a pure combinatorial point of view by Bondy and Hell (1990). In this paper we introduce strong and weak star chromatic numbers of uniform hypergraphs and study their basic properties. In particular, we focus on partial Steiner triple systems (PSTSs) for the weak case. We also discuss the computational complexity of finding a (k, d)-colouring for a PSTS and construct, for every rational k/d > 2, a k/d star chromatic PSTS.