English

Chv\'atal-Erd\H{o}s condition for pancyclicity

Combinatorics 2023-01-25 v1

Abstract

An nn-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 33 up to nn. 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 GG with κ(G)>(1+o(1))α(G)\kappa(G) > (1+o(1)) \alpha(G) is pancyclic. This extends the famous Chv\'atal-Erd\H{o}s condition for Hamiltonicity and proves asymptotically a 3030-year old conjecture of Jackson and Ordaz.

Keywords

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}
}
R2 v1 2026-06-28T08:18:55.743Z