Abstract
Erdős, Faber and Lovász conjectured in 1972 that the vertices of a linear hypergraph with n edges, each of size n, can be strongly colored with n colors. It was shown by Romero and Sánchez-Arroyo that an equivalent conjecture is obtained when linear hypergraphs are replaced by n-clusters. In this paper we describe new families of EFL-compliant n-clusters; that is, those for which the conjecture holds. Moreover, we describe ways to extend some n-clusters to larger ones preserving EFL-compliance. Also, our approach allowed us to provide a new upper bound for the chromatic number of n-clusters.
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On sabbatical leave at: Instituto Tecnológico de Monterrey, Nuevo León, Mexico.
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Calvillo, G., Romero, D. New Families of n-Clusters Verifying the Erdős–Faber–Lovász Conjecture. Graphs and Combinatorics 32, 2241–2252 (2016). https://doi.org/10.1007/s00373-016-1733-8
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DOI: https://doi.org/10.1007/s00373-016-1733-8