Chromatic numbers of hypergraphs and coverings of graphs

Burr recently proved [3] that for positive integers m 1 , m 2 …… m k , and any graph G we have X(G)\documentclass{article}\pagestyle{empty}\begin{document}$ \chi (G)\, \le \,\mathop \prod \limits_{i = 1}^k m_i $\end{document}if and only if G can be expressed as the edge disjoint union of subgraphs F i satisfying X(F i ) ≤ m i . This theorem is generalized to hypergraphs. By suitable interpretations the generalization is then used to deduce propositions on coverings of graphs.