Regularity, uniformity, and quasirandomness
نویسندگان
چکیده
منابع مشابه
Regularity, 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...
متن کاملHereditary quasirandomness without regularity
A result of Simonovits and Sós states that for any fixed graph H and any ǫ > 0 there exists δ > 0 such that if G is an n-vertex graph with the property that every S ⊆ V (G) contains p|S|± δn labeled copies of H , then G is quasirandom in the sense that every S ⊆ V (G) contains 12p|S| 2 ± ǫn edges. The original proof of this result makes heavy use of the regularity lemma, resulting in a bound on...
متن کاملQuasirandomness and Regularity: Lecture Notes Iv
One of the most beautiful, and useful, areas in which quasirandomness has been studied concerns the subsets of the (rational) integers modulo n, which we write Zn. We need a few items of notation before introducing the random-like properties we are interested in. First of all, for x ∈ Zn, let en(x) = e. When n is understood, we simply write e(x). Then, for a subset S ⊂ Zn, let the function χS :...
متن کاملQuasirandomness and Regularity: Lecture Notes I
The idea behind quasirandomness is that many random-like properties of combinatorial objects are equivalent, although they often do not appear to be so on first glance. We begin with the first class to which this notion was applied, and perhaps the most studied of combinatorial objects, graphs. It is easy to show that each of the following properties are true with probability 1 of a uniformly c...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2005
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.0503263102