The largest hole in sparse random graphs

Nemanja Draganić, Stefan Glock*, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)666-677
Number of pages12
JournalRandom Structures and Algorithms
Issue number4
StatePublished - Feb 2022


FundersFunder number
USA-Israel BSF2018267
Walter Haefner Foundation
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Eidgenössische Technische Hochschule Zürich
Israel Science Foundation1261/17
ETH Zürich Foundation


    • hole
    • induced path
    • random graph


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