A hypergraph is intersecting if any two different edges have exactly one common vertex, and an \(n\)-quasicluster is an intersecting hypergraph with \(n\) edges, each one containing at most \(n\) vertices, and every vertex is contained in at least two edges. The Erdős-Faber-Lovász Conjecture states that the chromatic number of any \(n\)-quasicluster is at most \(n\). In the present note, we prove the correctness of the conjecture for a new infinite class of \(n\)-quasiclusters using a specific edge coloring of the complete graph.
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