Coloring simple hypergraphs

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Abstract

Fix an integer k3. 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 satisfyingχ(H)<c(ΔlogΔ)1k1. 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.

Keywords

Hypergraph coloring
Semi-random method

Cited by (0)

1

Supported in part by NSF Grants DMS-0753472 and CCF-1013110.

2

Supported in part by NSF Grants DMS-0653946, 0969092, 1300138.