Defective Colouring of Hypergraphs

We prove that the vertices of every $(r+1)$-uniform hypergraph with maximum degree $\mathrm{\Delta }$ may be coloured with $c(\frac{\mathrm{\Delta }}{d+1}{)}^{1\mathrm{/}r}$ colours such that each vertex is in at most $d$ monochromatic edges. This result, which is best possible up to the value of the constant $c$, generalises the classical result of Erdős and Lovász who proved the $d=0$ case.