Israel Journal of Mathematics

, Volume 229, Issue 1, pp 269–285 | Cite as

Long cycles in Hamiltonian graphs

  • António Girão
  • Teeradej Kittipassorn
  • Bhargav NarayananEmail author


We prove that if an n-vertex graph with minimum degree at least 3 contains a Hamiltonian cycle, then it contains another cycle of length no(n); in particular, this verifies, in an asymptotic form, a well-known conjecture due to Sheehan from 1975.


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • António Girão
    • 1
  • Teeradej Kittipassorn
    • 2
  • Bhargav Narayanan
    • 3
    Email author
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK
  2. 2.Department of Mathematics and Computer Science, Faculty of ScienceChulalongkorn UniversityBangkokThailand
  3. 3.Department of MathematicsRutgers UniversityPiscatawayUSA

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