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 Erdős 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.