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Coloring simple hypergraphs

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journal contribution
posted on 27.06.2013 by Alan Frieze, Dhruv Mubayi

Fix an integer k⩾3k⩾3. A k-uniform hypergraph is simple if every two edges share at most one vertex. We prove that there is a constant c depending only on k such that every simple k-uniform hypergraph H with maximum degree Δ has chromatic number satisfying

This implies a classical result of Ajtai, Komlós, Pintz, Spencer and Szemerédi and its strengthening due to Duke, Lefmann and Rödl. The result is sharp apart from the constant c.

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Publisher Statement

This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.jctb.2013.09.003

Date

27/06/2013

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