The Erdős–Faber–Lovász conjecture for dense hypergraphs Original Research Article

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 image. A well-known conjecture of Erdős, Faber and Lovász states that if a linear hypergraph, image, 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 image by deleting the vertices of degree one is dense.