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.
@article{bwmeta1.element.doi-10_7151_dmgt_1781,
author = {John Bosica and Claude Tardif},
title = {Fractional Aspects of the Erd\H os-Faber-Lov\'asz Conjecture},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {197-202},
zbl = {1307.05186},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1781}
}
John Bosica; Claude Tardif. Fractional Aspects of the Erdős-Faber-Lovász Conjecture. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 197-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1781/
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