ADVANCES ON THE ERDŐS–FABER–LOVÁSZ CONJECTURE
A hypergraph is linear if no two distinct edges intersect in more than one vertex. A well-known conjecture of Erdős, Faber, and Lovász states that if a linear hypergraph has n edges, each of size n, then there is a n-vertex colouring of the hypergraph such that each edge contains one vertex of each colour. Dating back to 1972, it is very surprising that this conjecture has not been settled in its full generality. This chapter presents some advances on it.
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