منابع مشابه
The poset of hypergraph quasirandomness
Chung and Graham began the systematic study of hypergraph quasirandom properties soon after the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs. One feature that became apparent in the early work on hypergraph quasirandomness is that properties that are equivalent for graphs are not equivalent for hypergraphs, and thus hypergraphs enjoy a variety of inequivalent q...
متن کاملCounting Cycles to Efficiently Certify Sparse Hypergraph Quasirandomness
One surprising property of Chung, Graham, and Wilson’s characterization of dense quasirandom graphs is a polynomial-time verifiable property Cycle4, which states that the number of copies of the cycle of length four is what one would expect in a random graph of the same density. Targeting problems like random k-SAT, this algorithm has been extended in several ways to sparse quasirandomness by s...
متن کاملQuasirandomness and Gowers’ Theorem
“Quasirandomness” will be described and the Quasirandomness Theorem will be used to prove Gowers’ Theorem. This article assumes some familiarity with linear algebra and elementary probability theory.
متن کاملSzemerédi's Partition and Quasirandomness
In this paper we shall investigate the connection between the SzemerCdi Regularity Lemma and quasirandom graph sequences, defined by Chung, Graham, and Wilson, and also, slightly differently, by Thomason. We prove that a graph sequence (G,) is quasirandom if and only if in the SzemerCdi partitions of G , almost all densities are $ + o(1). Many attempts have been made to clarify when an individu...
متن کاملRegularity, uniformity, and quasirandomness.
G raph theory is the appropriate language for discussing binary relations on objects. Results in graph theory have numerous applications in biology, chemistry, computer science, and physics. In cases of multiple relations, instead of binary relations more general structures known as hypergraphs are the right tools. However, it turns out that because of their extremely complex structure, hypergr...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2013
ISSN: 1042-9832
DOI: 10.1002/rsa.20521