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Improved bounds and algorithms for hypergraph two-coloring

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2 Author(s)
J. Radhakrishnan ; Sch. of Technol. & Comput. Sci., Tata Inst. of Fundamental Res., Mumbai, India ; A. Srinivasan

We show that for all large n, every n-uniform hypergraph with at most 0.7√(n/lnn)×2n edges can be two-colored. We, in fact, present fast algorithms that output a proper two-coloring with high probability for such hypergraphs. We also derandomize and parallelize these algorithms, to derive NC1 versions of these results. This makes progress on a problem of Erdos (1963), improving the previous-best bound of n1/3-0(1)×2n due to Beck (1978). We further generalize this to a “local” version, improving on one of the first applications of the Lovasz Local Lemma

Published in:

Foundations of Computer Science, 1998. Proceedings. 39th Annual Symposium on

Date of Conference:

8-11 Nov 1998