A hypergraph, having n edges, is linear if no two distinct edges intersect in more than one vertex, and is dense if its minimum degree is greater than n. A well-known conjecture of Erdős, Faber and Lovász states that if a linear hypergraph, H, has n edges, each of size n, then there is a n-vertex colouring of the hypergraph in such a way that each edge contains vertices of all the colours. In this note we present a proof of the conjecture provided the hypergraph obtained from H by deleting the vertices of degree one is dense.
Sánchez-Arroyo, A. (2007). The Erdős–Faber–Lovász conjecture for dense hypergraphs. Discrete Mathematics, 308(5–6), 991–992. https://doi.org/10.1016/j.disc.2007.09.026