Semi-Strong Colouring of Intersecting Hypergraphs.

For any c >= 2, a c-strong colouring of the hypergraph G is an assignment of colours to the vertices of G such that, for every edge e of G, the vertices of e are coloured by at least min{c, |e|} distinct colours. The hypergraph G is t-intersecting if every two edges of G have at least t vertices in common. A natural variant of a question of Erdos and Lovasz is: For fixed c >= 2 and t >= 1, what is the minimum number of colours that is sufficient to c-strong colour any t-intersecting hypergraphs? The purpose of this note is to describe some open problems related to this question.