Cayley Graphs Of Order $pqrs$ Are Hamiltonian

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 $pqrs$.