Cycles of Many Lengths in Hamiltonian Graphs

Matija Bucić, Lior Gishboliner, Benny Sudakov

Research output: Chapter in Book/Report/Conference proceedingChapter


In 1999, Jacobson and Lehel conjectured that for k≥ 3, every k-regular Hamiltonian graph has cycles of at least linearly many different lengths. This was further strengthened by Verstraëte, who asked whether the regularity can be replaced with the weaker condition that the minimum degree is at least 3. Despite attention from various researchers, until now the best partial result towards both of these conjectures was a n lower bound on the number of cycle lengths. We resolve these conjectures asymptotically, by showing that the number of cycle lengths is at least n1 - o ( 1 ).

Original languageEnglish (US)
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages7
StatePublished - 2021
Externally publishedYes

Publication series

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

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Cycle lengths
  • Cycle spectrum
  • Hamiltonian graph


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