Long cycles in Hamiltonian graphs
Combinatorics
2017-09-19 v2
Abstract
We prove that if an -vertex graph with minimum degree at least contains a Hamiltonian cycle, then it contains another cycle of length ; 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.
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