On the upper chromatic number of (v3,b2)-configurations Original Research Article

A mixed hypergraph is a pair H=(V,E∪A), where V is the vertex set and E (A) the edge (the co-edge) set of H. A legal colouring of H gives the same (different) colour(s) to at least two vertices of any co-edge (of any edge). The upper chromatic number of H is the maximum number χ̄(H) of colours that can be used in a legal colouring. After giving a general upper bound to χ̄(H), we here consider the co-hypergraph S=(X,∅∪T), where T is a (v3,b2)-configuration T over X. We prove that computing χ̄(S) is NP-hard, but there exists a polynomial-time algorithm returning a colouring with ⩾56χ̄(S) colours. We also provide an example showing that this approximation factor is tight.