Defective Colouring of Hypergraphs

We prove that the vertices of every $(r + 1)$-uniform hypergraph with maximum degree $Δ$ may be coloured with $c(\fracΔ{d + 1})^{1/r}$ 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.

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