The Largest Hole in Sparse Random Graphs

Nemanja Draganić, Stefan Glock, Michael Krivelevich

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-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 languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages45-49
Number of pages5
DOIs
StatePublished - 2021

Publication series

NameTrends in Mathematics
Volume14
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Keywords

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

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