Hamiltonian cycles in Cayley graphs whose order has few prime factors - Kutnar, Klavdija (Ars mathematica contemporanea, 2012)
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 ?$24 \ne k < 32$?, or of the form ?$kpq$? with ?$k \le 5$?, or of the form ?$pqr$?, or of the form ?$kp^2$? with ?$k \le 4$?, or of the form ?$kp^3$? with ?$k \le 2$?.
Keywords: Cayley graphs; Cayleyjevi grafi; graph theory; hamiltonian cycles; hamiltonski cikli; teorija grafov