An Algorithmic Hypergraph Regularity Lemma

Abstract

Szemerédi’s Regularity Lemma is a powerful tools in graph theory. It asserts that all large graphs admit bounded partitions of their edge sets, most classes of which consist of uniformly distributed edges. The original proof of this result was non-constructive and a constructive proof was later given by Alon, Duke, Lefmann, Rödl and Yuster. Szemerédi’s Regularity Lemma was extended to hypergraphs by various authors. Frankl and Rödl gave one such extension in the case of 3-uniform hypergraphs, which was later extended to k-uniform hypergraphs by Rödl and Skokan. W.T. Gowers gave another such extension, using a different concept of regularity than that of Frankl, Rödl and Skokan. In this paper, we give a constructive proof of the Regularity Lemma for hypergraphs