Hamiltonian cycles in Caley 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 6= 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.