Large Induced Matchings in Random Graphs

Oliver Cooley; Nemanja Dragani; Mihyun Kang; Benny Sudakov

doi:10.1137/20M1330609

Large Induced Matchings in Random Graphs

Oliver Cooley, Nemanja Dragani, Mihyun Kang, Benny Sudakov

Institute of Discrete Mathematics (5050)

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

Abstract

Given a large graph H, does the binomial random graph G(n, p) contain a copy of H as an induced subgraph with high probability? This classical question has been studied extensively for various graphs H, going back to the study of the independence number of G(n, p) by Erd\H os and Bollob\'as and by Matula in 1976. In this paper we prove an asymptotically best possible result for induced matchings by showing that if C/n \leq p \leq 0.99 for some large constant C, then G(n, p) contains an induced matching of order approximately 2 logq(np), where q = 1 1 p .

Original language	English
Pages (from-to)	267-280
Number of pages	14
Journal	SIAM Journal on Discrete Mathematics
Volume	35
Issue number	1
DOIs	https://doi.org/10.1137/20M1330609 https://doi.org/10.1137/20M1330609
Publication status	Published - 2021

Keywords

Induced matchings
Paley-zygmund inequality
Random graphs
Talagrand's inequality

ASJC Scopus subject areas

General Mathematics

Fields of Expertise

Information, Communication & Computing

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Cite this

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title = "Large Induced Matchings in Random Graphs",

abstract = "Given a large graph H, does the binomial random graph G(n, p) contain a copy of H as an induced subgraph with high probability? This classical question has been studied extensively for various graphs H, going back to the study of the independence number of G(n, p) by Erd\H os and Bollob\'as and by Matula in 1976. In this paper we prove an asymptotically best possible result for induced matchings by showing that if C/n \leq p \leq 0.99 for some large constant C, then G(n, p) contains an induced matching of order approximately 2 logq(np), where q = 1 1 p .",

keywords = "Induced matchings, Paley-zygmund inequality, Random graphs, Talagrand's inequality",

author = "Oliver Cooley and Nemanja Dragani and Mihyun Kang and Benny Sudakov",

year = "2021",

doi = "10.1137/20M1330609",

language = "English",

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pages = "267--280",

journal = "SIAM Journal on Discrete Mathematics",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - Large Induced Matchings in Random Graphs

AU - Cooley, Oliver

AU - Dragani, Nemanja

AU - Kang, Mihyun

AU - Sudakov, Benny

PY - 2021

Y1 - 2021

N2 - Given a large graph H, does the binomial random graph G(n, p) contain a copy of H as an induced subgraph with high probability? This classical question has been studied extensively for various graphs H, going back to the study of the independence number of G(n, p) by Erd\H os and Bollob\'as and by Matula in 1976. In this paper we prove an asymptotically best possible result for induced matchings by showing that if C/n \leq p \leq 0.99 for some large constant C, then G(n, p) contains an induced matching of order approximately 2 logq(np), where q = 1 1 p .

AB - Given a large graph H, does the binomial random graph G(n, p) contain a copy of H as an induced subgraph with high probability? This classical question has been studied extensively for various graphs H, going back to the study of the independence number of G(n, p) by Erd\H os and Bollob\'as and by Matula in 1976. In this paper we prove an asymptotically best possible result for induced matchings by showing that if C/n \leq p \leq 0.99 for some large constant C, then G(n, p) contains an induced matching of order approximately 2 logq(np), where q = 1 1 p .

KW - Induced matchings

KW - Paley-zygmund inequality

KW - Random graphs

KW - Talagrand's inequality

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VL - 35

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EP - 280

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -

Large Induced Matchings in Random Graphs

Abstract

Keywords

ASJC Scopus subject areas

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FWF - Cores - Random Graphs: Cores, Colourings and Contagion

Cite this

Large Induced Matchings in Random Graphs

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Projects

FWF - Cores - Random Graphs: Cores, Colourings and Contagion

Cite this