Geodesic
On 2-factors with long cycles in cubic graphs
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 79-93.

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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.
DOI : 10.26493/1855-3974.194.abe
Keywords: Cubic graph, 2-factor, long cycle, snark, infinite graph 
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André Kündgen; R. Bruce Richter. On 2-factors with long cycles in cubic graphs. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 79-93. doi : 10.26493/1855-3974.194.abe. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.194.abe/

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