Embedding graphs with bounded degree in sparse pseudorandom graphs

Kohayakawa, Yoshiharu; Rödl, Vojtěch; Sissokho, Papa A.

doi:10.1007/bf02787543

Cited by 12 publications

(24 citation statements)

References 18 publications

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“…In this section we state the adjusted version of one of the main results from [26] (see ( * )) discussed in Section 3.2. Given an -partite graph H with -partition…”

Section: An Embedding Lemma For -Partite Bi-jumbled Graphsmentioning

confidence: 98%

“…Going from PAIR to TUPLE(d H ) is also an important step in the proof of ( * ). For this step, hypothesis BDD is used in [26]; here, in the proof of Proposition 12, we again replace BDD with the local sparseness of the B r .…”

Section: The Embedding Lemmamentioning

confidence: 99%

“…In this paper, roughly speaking, we follow an approach in [26]. An embedding lemma in [26] is as follows:…”

Section: An Outline Of the Proof Of Theoremmentioning

confidence: 99%

“…Hence we must define δ and γ and, for a given p = p(n), we must also define N 0 and then show that this choice is correct. Our proof uses a technique from [26,30] (see Lemma 26 and the proof of Lemma 43 in [26]) and is based on the following lemma, which is a well-known consequence of the Cauchy-Schwarz inequality. …”

mentioning

confidence: 99%

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Turán's theorem for pseudo-random graphs

Kohayakawa

Rödl

Schacht

et al. 2007

Journal of Combinatorial Theory, Series A

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“…In this section we state the adjusted version of one of the main results from [26] (see ( * )) discussed in Section 3.2. Given an -partite graph H with -partition…”

Section: An Embedding Lemma For -Partite Bi-jumbled Graphsmentioning

confidence: 98%

Section: The Embedding Lemmamentioning

confidence: 99%

“…In this paper, roughly speaking, we follow an approach in [26]. An embedding lemma in [26] is as follows:…”

Section: An Outline Of the Proof Of Theoremmentioning

confidence: 99%

mentioning

confidence: 99%

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Turán's theorem for pseudo-random graphs

Kohayakawa

Rödl

Schacht

et al. 2007

Journal of Combinatorial Theory, Series A

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show abstract

“…We establish a so-called counting lemma that allows embeddings of certain linear uniform hypergraphs into sparse pseudorandom hypergraphs, generalizing a result with the same density as G. In view of this result, the question arises to which extent it can be generalized to sparse pseudorandom graphs, and results in this direction can be found in [3][4][5]12]. We continue this line of research for embedding properties of sparse pseudorandom hypergraphs.…”

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confidence: 99%

Counting results for sparse pseudorandom hypergraphs I

Kohayakawa

Mota

Schacht

et al. 2017

European Journal of Combinatorics

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Abstract. We establish a so-called counting lemma that allows embeddings of certain linear uniform hypergraphs into sparse pseudorandom hypergraphs, generalizing a result with the same density as G. In view of this result, the question arises to which extent it can be generalized to sparse pseudorandom graphs, and results in this direction can be found in [3][4][5]12]. We continue this line of research for embedding properties of sparse pseudorandom hypergraphs. Counting lemmas for pseudorandom hypergraphs were also investigated by Conlon, Fox and Zhao [6].2010 Mathematics Subject Classification. 05C60 (primary), 05C65 (secondary).

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The poset of hypergraph quasirandomness

Lenz

Mubayi

2013

Random Struct Algorithms

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Chung and Graham began the systematic study of k-uniform hypergraph quasirandom properties soon after the foundational results of Thomason and Chung-GrahamWilson on quasirandom graphs. One feature that became apparent in the early work on k-uniform hypergraph quasirandomness is that properties that are equivalent for graphs are not equivalent for hypergraphs, and thus hypergraphs enjoy a variety of inequivalent quasirandom properties. In the past two decades, there has been an intensive study of these disparate notions of quasirandomness for hypergraphs, and an open problem that has emerged is to determine the relationship between them.Our main result is to determine the poset of implications between these quasirandom properties. This answers a recent question of Chung and continues a project begun by Chung and Graham in their first paper on hypergraph quasirandomness in the early 1990's.

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Embedding graphs with bounded degree in sparse pseudorandom graphs

Cited by 12 publications

References 18 publications

Turán's theorem for pseudo-random graphs

Turán's theorem for pseudo-random graphs

Counting results for sparse pseudorandom hypergraphs I

The poset of hypergraph quasirandomness

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