The counting lemma for regular k-uniform hypergraphs
by
Brendan Nagle
,
Vojtěch Rödl
,
Mathias Schacht
| Citations: | 57 - 9 self |
BibTeX
@MISC{Nagle_thecounting,
author = {Brendan Nagle and Vojtěch Rödl and Mathias Schacht},
title = {The counting lemma for regular k-uniform hypergraphs },
year = {}
}
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Abstract
Abstract. Szemerédi’s Regularity Lemma proved to be a powerful tool in the area of extremal graph theory. Many of its applications are based on its accompanying Counting Lemma: If G is an ℓ-partite graph with V (G) = V1 ∪ · · · ∪ Vℓ and |Vi | = n for all i ∈ [ℓ], and all pairs (Vi, Vj) are ε-regular of density d for ℓ 1 ≤ i < j ≤ ℓ and ε ≪ d, then G contains (1 ± fℓ(ε))d 2 × nℓ cliques Kℓ, where fℓ(ε) → 0 as ε → 0.
