A note on the Erdos-Farber-Lovasz conjecture

A hypergraph H is linear if no two distinct edges of H intersect in more than one vertex and loopless if no edge has size one. A q-edge-colouring of H is a colouring of the edges of H with q colours such that intersecting edges receive different colours. We use Delta(H) to denote the maximum degree of H. A well-known conjecture of Erdos, Farber and Lovdsz is equivalent to the statement that every loopless linear hypergraph on n vertices can be n-edge-coloured. In this paper we show that the conjecture is true when the partial hypergraph S of H determined by the edges of size at least three can be Delta(S)-edge-coloured and satisfies Delta(S) <= 3. In particular, the conjecture holds when S is unimodular and Delta(S) <= 3. (c) 2006 Published by Elsevier B.V.