The largest hole in sparse random graphs

Nemanja Draganić; Stefan Glock; Michael Krivelevich

doi:10.1002/rsa.21078

The largest hole in sparse random graphs

Nemanja Draganić, Stefan Glock, Michael Krivelevich

School of Mathematical Sciences

Tel Aviv University

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

Abstract

We show that for any (Formula presented.) with (Formula presented.), with high probability, the size of a largest induced cycle in the random graph (Formula presented.) is (Formula presented.). This settles a long-standing open problem in random graph theory.

Original language	English
Pages (from-to)	666-677
Number of pages	12
Journal	Random Structures and Algorithms
Volume	61
Issue number	4
DOIs	https://doi.org/10.1002/rsa.21078
State	Published - Feb 2022

Keywords

hole
induced path
random graph

All Science Journal Classification (ASJC) codes

Software
General Mathematics
Computer Graphics and Computer-Aided Design
Applied Mathematics

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10.1002/rsa.21078

Cite this

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title = "The largest hole in sparse random graphs",

abstract = "We show that for any (Formula presented.) with (Formula presented.), with high probability, the size of a largest induced cycle in the random graph (Formula presented.) is (Formula presented.). This settles a long-standing open problem in random graph theory.",

keywords = "hole, induced path, random graph",

author = "Nemanja Dragani{\'c} and Stefan Glock and Michael Krivelevich",

note = "Publisher Copyright: {\textcopyright} 2022 The Authors. Random Structures & Algorithms published by Wiley Periodicals LLC.",

year = "2022",

month = feb,

doi = "10.1002/rsa.21078",

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AU - Glock, Stefan

AU - Krivelevich, Michael

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AB - We show that for any (Formula presented.) with (Formula presented.), with high probability, the size of a largest induced cycle in the random graph (Formula presented.) is (Formula presented.). This settles a long-standing open problem in random graph theory.

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U2 - 10.1002/rsa.21078

DO - 10.1002/rsa.21078

M3 - مقالة

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VL - 61

SP - 666

EP - 677

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 4

ER -

The largest hole in sparse random graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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