Hamiltonian cycles in Cayley graphs whose order has few prime factors

K. Kutnar, D. Marusic, D. W. Morris, J. Morris, P. Sparl

Published 2010-09-29, updated 2011-04-04Version 3

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 k < 32 and k not equal to 24, or of the form kpq with k < 6, or of the form pqr, or of the form kp^2 with k < 5, or of the form kp^3 with k < 3.