Geodesic
Fractional Aspects of the Erdős-Faber-Lovász Conjecture
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 197-202

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The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lovász conjecture, involving variations of the fractional chromatic number. We exhibit some relaxations that can be proved in the spirit of the Kahn-Seymour result, and others that are equivalent to the original conjecture.
Keywords: Erdős-Faber-Lovász Conjecture, fractional chromatic number 
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Bosica, John; Tardif, Claude. Fractional Aspects of the Erdős-Faber-Lovász Conjecture. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 197-202. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a15/