SOME CUBIC TIME REGULARITY ALGORITHMS FOR TRIPLE SYSTEMS

Szemeredi's regularity lemma guarantees that, for fixed epsilon >0, every graphG= (V,E)admits an epsilon -regular and t-equitable partition || (G), where t=O(1). These partitions are constructed by Kohayakawa, Rodl, and Thoma in time O(| V| (2)). Analogous partitions of k-graphs H((k))are constructed by Czygrinow and Rodl in time O(| V| (2k) - (1)log(5)| V| ). Fork= 3, we construct these partitions (and others with slightly stronger regularity) in timeO(| V| 3). We also discuss some applications.