منابع مشابه
On characterizing hypergraph regularity
Szemerédi’s Regularity Lemma is a well-known and powerful tool in modern graph theory. This result led to a number of interesting applications, particularly in extremal graph theory. A regularity lemma for 3-uniform hypergraphs developed by Frankl and Rödl [8] allows some of the Szemerédi Regularity Lemma graph applications to be extended to hypergraphs. An important development regarding Szeme...
متن کاملDissertation Defense On Algorithmic Hypergraph Regularity
Thomason and Chung, Graham and Wilson were the first to systematically study quasirandom graphs and hypergraphs and showed that several properties of random graphs imply each other in a deterministic sense. In particular, they showed that ε-regularity from Szemerédi’s regularity lemma is equivalent to their concepts. Over recent years several hypergraph regularity lemmas were established. In th...
متن کاملHypergraph regularity and quasi-randomness
Thomason and Chung, Graham, and Wilson were the first to systematically study quasi-random graphs and hypergraphs, and proved that several properties of random graphs imply each other in a deterministic sense. Their concepts of quasi-randomness match the notion of ε-regularity from the earlier Szemerédi regularity lemma. In contrast, there exists no “natural” hypergraph regularity lemma matchin...
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1. Ultrafilters, ultraproducts and ultralimits 1 1.1. Filters and ultrafilters 1 1.2. Ultralimits 2 1.3. Some model-theoretic notation 3 1.4. Ultraproducts of first-order structures 3 1.5. References 6 2. Graph regularity and measures on ultraproducts 6 2.1. Szemerédi’s regularity lemma 6 2.2. Finitely additive measures 7 2.3. Obtaining countable additivity 9 2.4. Integration for charges (signe...
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Szemerédi’s Regularity Lemma [22, 23] is a powerful tool in graph theory. It asserts that all large graphs G admit a bounded partition of E(G), most classes of which are bipartite subgraphs with uniformly distributed edges. The original proof of this result was non-constructive. A constructive proof was given by Alon, Duke, Lefmann, Rödl and Yuster [1], which allows one to efficiently construct...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2002
ISSN: 1042-9832
DOI: 10.1002/rsa.10058