Regular Partitions of Hypergraphs: Regularity Lemmas
نویسندگان
چکیده
Szemerédi’s regularity lemma for graphs has proved to be a powerful tool with many subsequent applications. The objective of this paper is to extend the techniques developed by Nagle, Skokan, and authors and obtain a stronger and more “user friendly” regularity lemma for hypergraphs.
منابع مشابه
Regular Partitions of Hypergraphs: Counting Lemmas
We continue the study of regular partitions of hypergraphs. In particular we obtain corresponding counting lemmas for the regularity lemmas for hypergraphs from [Regular partitions of hypergraphs: Regularity Lemmas, Combin. Probab. Comput., to appear].
متن کاملQuasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
The main results of this paper are regularity and counting lemmas for 3uniform hypergraphs. A combination of these two results gives a new proof of a theorem of Frankl and Rödl, of which Szemerédi’s theorem for arithmetic progressions of length 4 is a notable consequence. Frankl and Rödl also prove regularity and counting lemmas, but the proofs here, and even the statements, are significantly d...
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...
متن کاملRegularity Lemma for k-uniform hypergraphs
Szemerédi’s Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi-randomness, Random Structures and Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs and Combinatorics 8 (1992), 309–312, Extremal problems on set systems, Random Structures and A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 16 شماره
صفحات -
تاریخ انتشار 2007