Extremal results for odd cycles in sparse pseudorandom graphs

Elad Aigner-Horev; Hiêp Hàn; Mathias Schacht

doi:10.1016/j.endm.2013.10.060

Extremal results for odd cycles in sparse pseudorandom graphs

Elad Aigner-Horev, Hiêp Hàn, Mathias Schacht

Research output: Contribution to journal › Article › peer-review

Abstract

We consider extremal problems for subgraphs of pseudorandom graphs. Our results implies that for (n, d, λ)-graphs Γ satisfying. λ2k-1≪d2kn(logn)-2(k-1)(2k-1) any subgraph G⊂. Γ not containing a cycle of length 2. k+. 1 has relative density at most 12+o(1). Up to the polylog-factor the condition on λ is best possible and was conjectured by Krivelevich, Lee and Sudakov.

Original language	English
Pages (from-to)	385-391
Number of pages	7
Journal	Electronic Notes in Discrete Mathematics
Volume	44
DOIs	https://doi.org/10.1016/j.endm.2013.10.060
State	Published - 5 Nov 2013
Externally published	Yes

Keywords

Extremal graph theory
Odd cycles
Pseudorandom graphs

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.endm.2013.10.060

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title = "Extremal results for odd cycles in sparse pseudorandom graphs",

abstract = "We consider extremal problems for subgraphs of pseudorandom graphs. Our results implies that for (n, d, λ)-graphs Γ satisfying. λ2k-1≪d2kn(logn)-2(k-1)(2k-1) any subgraph G⊂. Γ not containing a cycle of length 2. k+. 1 has relative density at most 12+o(1). Up to the polylog-factor the condition on λ is best possible and was conjectured by Krivelevich, Lee and Sudakov.",

keywords = "Extremal graph theory, Odd cycles, Pseudorandom graphs",

author = "Elad Aigner-Horev and Hi{\^e}p H{\`a}n and Mathias Schacht",

year = "2013",

month = nov,

day = "5",

doi = "10.1016/j.endm.2013.10.060",

language = "English",

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journal = "Electronic Notes in Discrete Mathematics",

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T1 - Extremal results for odd cycles in sparse pseudorandom graphs

AU - Aigner-Horev, Elad

AU - Hàn, Hiêp

AU - Schacht, Mathias

PY - 2013/11/5

Y1 - 2013/11/5

N2 - We consider extremal problems for subgraphs of pseudorandom graphs. Our results implies that for (n, d, λ)-graphs Γ satisfying. λ2k-1≪d2kn(logn)-2(k-1)(2k-1) any subgraph G⊂. Γ not containing a cycle of length 2. k+. 1 has relative density at most 12+o(1). Up to the polylog-factor the condition on λ is best possible and was conjectured by Krivelevich, Lee and Sudakov.

AB - We consider extremal problems for subgraphs of pseudorandom graphs. Our results implies that for (n, d, λ)-graphs Γ satisfying. λ2k-1≪d2kn(logn)-2(k-1)(2k-1) any subgraph G⊂. Γ not containing a cycle of length 2. k+. 1 has relative density at most 12+o(1). Up to the polylog-factor the condition on λ is best possible and was conjectured by Krivelevich, Lee and Sudakov.

KW - Extremal graph theory

KW - Odd cycles

KW - Pseudorandom graphs

UR - https://www.scopus.com/pages/publications/84887167768

U2 - 10.1016/j.endm.2013.10.060

DO - 10.1016/j.endm.2013.10.060

M3 - Article

AN - SCOPUS:84887167768

SN - 1571-0653

VL - 44

SP - 385

EP - 391

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Extremal results for odd cycles in sparse pseudorandom graphs

Abstract

Keywords

ASJC Scopus subject areas

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