Coloring simple hypergraphs
نویسندگان
چکیده
Fix an integer k ≥ 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 ∆ has chromatic number satisfying χ(H) < c ( ∆ log ∆ ) 1 k−1 . This implies a classical result of Ajtai-Komlós-Pintz-Spencer-Szemerédi and its strengthening due to Duke-Lefmann-Rödl. The result is sharp apart from the constant c.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 103 شماره
صفحات -
تاریخ انتشار 2013