Improved bounds and algorithms for hypergraph 2-coloring

We show that for all large n, every n-uniform hypergraph with at most edges can be 2-colored. This makes progress on a problem of Erdos [Nordisk Mat. Tidskrift 11, 5–10 (1963)], improving the previous-best bound of n1/3−o(1)×2n due to Beck [Discrete Math. 24, 127–137 (1978)]. We further generalize this to a “local” version, improving on one of the first applications of the Lovasz local lemma. We also present fast randomized algorithms that output a proper 2-coloring with high probability for n-uniform hypergraphs with at most edges, for all large n. In addition, we derandomize and parallelize these algorithms, to derive NC1 versions of these results. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16: 4–32, 2000

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