Hamiltonian cycles in Cayley graphs whose order has few prime factorsKutnar, Klavdija (Avtor) Marušič, Dragan (Avtor) Morris, D. W. (Avtor) Morris, Joy (Avtor) Šparl, Primož (Avtor) graph theoryCayley graphshamiltonian cyclesWe 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 ▫$k \le 2$▫.20122013-10-15 12:09:08Neznano3760sl