Hamiltonian cycles in Cayley graphs whose order has few prime factors ## AbstractWe 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.
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