Hamiltonian cycles in Cayley graphs whose order has few prime factors

Abstract

We prove that if Cay(G; S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G; S) has a hamiltonian cycle. More precisely, if p, q, and r are distinct primes, then n can be of the form kp with 24 ≠ k < 32, or of the form kpq with k ≤ 5, or of the form pqr, or of the form kp² with k ≤ 4, or of the form kp³ with k ≤ 2.