Hamiltonian cycles in Caley graphs whose order has few prime factors
Morris, Dave Witte
Drustvo Matematikov, Fizikov in Astronomov
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.
Open access, licensed under Creative Commons
Caley graph , Hamiltonian cycles
Kutnar, K., Marusic, D., Morris, D. W., Morris, J., & Sparl, P. (2012). Hamiltonian cycles in Caley graphs whose order has few prime factors. Ars Mathematica Contemporanea, 5(1), 27-71