Chv\'atal-Erd\H{o}s condition for pancyclicity
Combinatorics
2023-01-25 v1
Abstract
An -vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices and it is pancyclic if it contains cycles of all lengths from up to . A celebrated meta-conjecture of Bondy states that every non-trivial condition implying Hamiltonicity also implies pancyclicity (up to possibly a few exceptional graphs). We show that every graph with is pancyclic. This extends the famous Chv\'atal-Erd\H{o}s condition for Hamiltonicity and proves asymptotically a -year old conjecture of Jackson and Ordaz.
Cite
@article{arxiv.2301.10190,
title = {Chv\'atal-Erd\H{o}s condition for pancyclicity},
author = {Nemanja Draganić and David Munhá Correia and Benny Sudakov},
journal= {arXiv preprint arXiv:2301.10190},
year = {2023}
}