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.
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