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Counting subgraphs in quasirandom 4uniform hypergraphs
 Random Structures and Algorithms, 2005 Volume 26, Issue 12 , Pages 160  203
"... Abstract. A bipartite graph G = (V1 ∪ V2, E) is (δ, d)regular if ˛ d − d(V ′ 1, V ′ 2) ˛ ˛ < δ whenever V ′ i ⊂ Vi, V ′ i  ≥ δVi, i = 1, 2. Here, d(V ′ ..."
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Cited by 8 (2 self)
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Abstract. A bipartite graph G = (V1 ∪ V2, E) is (δ, d)regular if ˛ d − d(V ′ 1, V ′ 2) ˛ ˛ < δ whenever V ′ i ⊂ Vi, V ′ i  ≥ δVi, i = 1, 2. Here, d(V ′
QuasiRandom Hypergraphs Revisited
"... ABSTRACT: The quasirandom theory for graphs mainly focuses on a large equivalent class of graph properties each of which can be used as a certificate for randomness. For kgraphs (i.e., kuniform hypergraphs), an analogous quasirandom class contains various equivalent graph properties including th ..."
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ABSTRACT: The quasirandom theory for graphs mainly focuses on a large equivalent class of graph properties each of which can be used as a certificate for randomness. For kgraphs (i.e., kuniform hypergraphs), an analogous quasirandom class contains various equivalent graph properties including
Bipartite Subgraphs and Quasirandomness
"... Abstract. We say that a family of graphs G = {Gn: n ≥ 1} is pquasirandom, 0 < p < 1, if it shares typical properties of the random graph G(n, p); for a definition, see below. We denote by Q w � (p) the class of all graphs H for which e(Gn) ≥ (1 + and the number of not necessarily induced la ..."
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Abstract. We say that a family of graphs G = {Gn: n ≥ 1} is pquasirandom, 0 < p < 1, if it shares typical properties of the random graph G(n, p); for a definition, see below. We denote by Q w � (p) the class of all graphs H for which e(Gn) ≥ (1 + and the number of not necessarily induced
Hypergraphs, QuasiRandomness, and Conditions for Regularity
 J. COMBIN. THEORY SER. A
, 2002
"... Haviland and Thomason and Chung and Graham were the rst to investigate systematically some properties of quasirandom hypergraphs. In particular, in a series of articles, Chung and Graham considered several quite disparate properties of randomlike hypergraphs of density 1=2 and proved that they are ..."
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Cited by 38 (9 self)
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that they are in fact equivalent. The central concept in their work turned out to be the so called deviation of a hypergraph. They proved that having small deviation is equivalent to a variety of other properties that describe quasirandomness. In this paper, we consider the concept of discrepancy for kuniform
Weak quasirandomness for uniform hypergraphs
, 2009
"... We study quasirandom properties of kuniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known ChungGrahamWilson theorem fo ..."
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Cited by 22 (8 self)
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We study quasirandom properties of kuniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known ChungGrahamWilson theorem
Quasirandom hypergraphs revisited  Corrigendum: Quasirandom classes of hypergraphs, Random Structures and Algorithms 1 (1990), 363–382.
"... The quasirandom theory for graphs mainly focuses on a large equivalent class of graph properties each of which can be used as a certificate for randomness. For kgraphs (i.e., kuniform hypergraphs), an analogous quasirandom class contains various equivalent graph properties including the kdiscre ..."
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The quasirandom theory for graphs mainly focuses on a large equivalent class of graph properties each of which can be used as a certificate for randomness. For kgraphs (i.e., kuniform hypergraphs), an analogous quasirandom class contains various equivalent graph properties including the k
MORE ON QUASIRANDOM GRAPHS, SUBGRAPH COUNTS AND GRAPH LIMITS
"... Abstract. We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It has been shown by several authors that several suc ..."
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such conditions are quasirandom, but that there are exceptions. In order to understand this better, we investigate some new properties of this type. We show that these properties too are quasirandom, at least in some cases; however, there are also cases that are left as open problems, and we discuss why
The QuasiRandomness of Hypergraph Cut Properties
"... Let α1,..., αk satisfy ∑ i αi = 1 and suppose a kuniform hypergraph on n vertices satisfies the following property; in any partition of its vertices into k sets A1,..., Ak of sizes α1n,..., αkn, the number of edges intersecting A1,..., Ak is (asymptotically) the number one would expect to find in a ..."
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in a random kuniform hypergraph. Can we then infer that H is quasirandom? We show that the answer is negative if and only if α1 = · · · = αk = 1/k. This resolves an open problem raised in 1991 by Chung and Graham [J. AMS ’91]. While hypergraphs satisfying the property corresponding to α1
Results 1  10
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77,285