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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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