2016/05/11 by Araujo-Pardo, Gabriela, Vázquez-Ávila, Adrián
#05C15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1605.03374
A linear hypergraph is intersecting if any two different edges have exactly one common vertex and an n-quasicluster is an intersecting linear hypergraph with n edges each one containing at most n vertices and every vertex is contained in at least two edges. The Erdös-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.