On 2-factors with long cycles in cubic graphs

André Kündgen, R. Bruce Richter

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.

Keywords


Cubic graph, 2-factor, long cycle, snark, infinite graph

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DOI: https://doi.org/10.26493/1855-3974.194.abe

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications