 Hypergraph chromatic index

The chromatic index of a hypergraph is the minimum number of colours needed to colour its edges so that intersecting edges have different colours. Each colour class is a matching in a hypergraph. It is at least the maximum hypergraph vertex degree, and at most $r(\Delta -1)+1$ for an $r$-uniform hypergraph of maximum degree $\Delta$, by greedily colouring edges: an edge meets at most $r(\Delta -1)$ others.