Cayley Graphs Of Order $pqrs$ Are Hamiltonian

Florian Lehner; Farzad Maghsoudi; Bobby Miraftab

Cayley Graphs Of Order $pqrs$ Are Hamiltonian

Combinatorics 2026-07-16 v1

Authors: Florian Lehner , Farzad Maghsoudi , Bobby Miraftab

Abstract

Assume $G$ is a finite group with order $|G| = pqrs$ , where $p$ , $q$ , $r$ , and $s$ are distinct prime numbers. We prove that every connected Cayley graph of $G$ contains a hamiltonian cycle. Our result drops all restrictions of all previously known results on hamiltonian cycles in Cayley graphs of groups of order $pqrs$ .

Keywords

Cayley graph Hamiltonian cycle finite group prime order connected graph

Cite

@article{arxiv.2607.14440,
  title  = {Cayley Graphs Of Order $pqrs$ Are Hamiltonian},
  author = {Florian Lehner and Farzad Maghsoudi and Bobby Miraftab},
  journal= {arXiv preprint arXiv:2607.14440},
  year   = {2026}
}