---
_id: '13042'
abstract:
- lang: eng
  text: Let Lc,n denote the size of the longest cycle in G(n, c/n),c >1 constant.  We
    show that there exists a continuous function f(c) such that Lc,n/n→f(c) a.s.  for
    c>20,  thus  extending  a  result  of  Frieze  and  the  author  to  smaller  values  of
    c. Thereafter,  for c>20,  we  determine  the  limit  of  the  probability  that
    G(n, c/n)contains  cycles  of  every  length  between  the  length  of  its  shortest  and  its  longest
    cycles as n→∞.
acknowledgement: We would like to thank the reviewers for their helpful comments and
  remarks.
article_number: P2.21
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Anastos, Michael
  id: 0b2a4358-bb35-11ec-b7b9-e3279b593dbb
  last_name: Anastos
citation:
  ama: Anastos M. A note on long cycles in sparse random graphs. <i>Electronic Journal
    of Combinatorics</i>. 2023;30(2). doi:<a href="https://doi.org/10.37236/11471">10.37236/11471</a>
  apa: Anastos, M. (2023). A note on long cycles in sparse random graphs. <i>Electronic
    Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/11471">https://doi.org/10.37236/11471</a>
  chicago: Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic
    Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2023. <a href="https://doi.org/10.37236/11471">https://doi.org/10.37236/11471</a>.
  ieee: M. Anastos, “A note on long cycles in sparse random graphs,” <i>Electronic
    Journal of Combinatorics</i>, vol. 30, no. 2. Electronic Journal of Combinatorics,
    2023.
  ista: Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic
    Journal of Combinatorics. 30(2), P2.21.
  mla: Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic
    Journal of Combinatorics</i>, vol. 30, no. 2, P2.21, Electronic Journal of Combinatorics,
    2023, doi:<a href="https://doi.org/10.37236/11471">10.37236/11471</a>.
  short: M. Anastos, Electronic Journal of Combinatorics 30 (2023).
corr_author: '1'
date_created: 2023-05-21T22:01:05Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2024-10-09T21:05:26Z
day: '05'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/11471
external_id:
  arxiv:
  - '2105.13828'
  isi:
  - '000988285500001'
file:
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  creator: dernst
  date_created: 2023-05-22T07:43:19Z
  date_updated: 2023-05-22T07:43:19Z
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file_date_updated: 2023-05-22T07:43:19Z
has_accepted_license: '1'
intvolume: '        30'
isi: 1
issue: '2'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on long cycles in sparse random graphs
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 30
year: '2023'
...