On 2-factors with long cycles in cubic graphs - Kündgen, André (Ars mathematica contemporanea, 2011)
Every 2-connected cubic graph ?$G$? has a 2-factor, and much effort has gone into studying conditions that guarantee ?$G$? to be Hamiltonian. We show that if ?$G$? is not Hamiltonian, then ?$G$? is either the Petersen graph or contains a 2-factor with a cycle of length at least 7. We also give infinite families of, respectively, 2- and 3-connected cubic graphs in which every 2-factor consists of cycles of length at most, respectively, 10 and 16.
Keywords: 2-factor; 2-faktor; cubic graph; dolg cikel; graph theory; infinite graph; kubični grafi; long cycle; neskončen graf; snark; teorija grafov