English

Long cycles in Hamiltonian graphs

Combinatorics 2017-09-19 v2

Abstract

We prove that if an nn-vertex graph with minimum degree at least 33 contains a Hamiltonian cycle, then it contains another cycle of length no(n)n-o(n); this implies, in particular, that a well-known conjecture of Sheehan from 1975 holds asymptotically. Our methods, which combine constructive, poset-based techniques and non-constructive, parity-based arguments, may be of independent interest.

Keywords

Cite

@article{arxiv.1709.04895,
  title  = {Long cycles in Hamiltonian graphs},
  author = {António Girão and Teeradej Kittipassorn and Bhargav Narayanan},
  journal= {arXiv preprint arXiv:1709.04895},
  year   = {2017}
}

Comments

15 pages, submitted, some typos fixed

R2 v1 2026-06-22T21:43:29.395Z