The Largest Hole in Sparse Random Graphs

Nemanja Draganić, Stefan Glock, Michael Krivelevich

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 languageEnglish
Title of host publicationExtended Abstracts EuroComb 2021
Subtitle of host publicationEuropean Conference on Combinatorics, Graph Theory and Applications
EditorsJaroslav Nešetřil, Juanjo Rué, Guillem Perarnau, Oriol Serra
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages5
ISBN (Electronic)978-3-030-83823-2
ISBN (Print)978-3-030-83822-5
StatePublished - 2021

Publication series

NameTrends in Mathematics


  • Hole
  • Induced path
  • Random graph
  • Second moment method

All Science Journal Classification (ASJC) codes

  • General Mathematics


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