The Largest Hole in Sparse Random Graphs

Nemanja Draganić; Stefan Glock; Michael Krivelevich

doi:10.1007/978-3-030-83823-2_8

The Largest Hole in Sparse Random Graphs

Nemanja Draganić, Stefan Glock^*, Michael Krivelevich

^*Corresponding author for this work

School of Mathematical Sciences

ETH Zurich

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We show that for d≥ d₀(ϵ), with high probability, the size of a largest induced cycle in the random graph G(n, d/n) is (2±ϵ)ndlogd. This settles a long-standing open problem in random graph theory.

Original language	English
Title of host publication	Extended Abstracts EuroComb 2021
Subtitle of host publication	European Conference on Combinatorics, Graph Theory and Applications
Editors	Jaroslav Nešetřil, Juanjo Rué, Guillem Perarnau, Oriol Serra
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	45-49
Number of pages	5
ISBN (Electronic)	978-3-030-83823-2
ISBN (Print)	978-3-030-83822-5
DOIs	https://doi.org/10.1007/978-3-030-83823-2_8
State	Published - 2021

Publication series

Name	Trends in Mathematics
Volume	14
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Keywords

Hole
Induced path
Random graph
Second moment method

Access to Document

10.1007/978-3-030-83823-2_8

Cite this

Draganić, N., Glock, S., & Krivelevich, M. (2021). The Largest Hole in Sparse Random Graphs. In J. Nešetřil, J. Rué, G. Perarnau, & O. Serra (Eds.), Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications (pp. 45-49). (Trends in Mathematics; Vol. 14). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-83823-2_8

Draganić, Nemanja ; Glock, Stefan ; Krivelevich, Michael. / The Largest Hole in Sparse Random Graphs. Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications. editor / Jaroslav Nešetřil ; Juanjo Rué ; Guillem Perarnau ; Oriol Serra. Springer Science and Business Media Deutschland GmbH, 2021. pp. 45-49 (Trends in Mathematics).

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Draganić, N, Glock, S & Krivelevich, M 2021, The Largest Hole in Sparse Random Graphs. in J Nešetřil, J Rué, G Perarnau & O Serra (eds), Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications. Trends in Mathematics, vol. 14, Springer Science and Business Media Deutschland GmbH, pp. 45-49. https://doi.org/10.1007/978-3-030-83823-2_8

The Largest Hole in Sparse Random Graphs. / Draganić, Nemanja; Glock, Stefan; Krivelevich, Michael.
Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications. ed. / Jaroslav Nešetřil; Juanjo Rué; Guillem Perarnau; Oriol Serra. Springer Science and Business Media Deutschland GmbH, 2021. p. 45-49 (Trends in Mathematics; Vol. 14).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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T1 - The Largest Hole in Sparse Random Graphs

AU - Draganić, Nemanja

AU - Glock, Stefan

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KW - Induced path

KW - Random graph

KW - Second moment method

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The Largest Hole in Sparse Random Graphs

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Keywords

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