On the Erdos-Faber-Lovasz Conjecture

Abstract

In \(1972\), Erdős, Faber, and Lovász made the now famous conjecture: If a graph \(G\) consists of \(n\) copies of the complete graph \(K_n\), such that any two copies have at most one common vertex (such graphs are called EFL graphs), then \(G\) is \(n\)-colorable. In this paper, we show that the conjecture is true for two different classes of EFL graphs. Furthermore, a new shorter proof of the conjecture is given for a third class of EFL graphs.