On 2-factors with long cycles in cubic graphs

Abstract

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.