Circuits of length 5 in 2-factors of cubic graphs

For every even integer n≥28 we construct a cyclically 4-edge-connected snark of order n which has girth 5 and contains a 5-circuit in every 2-factor. In addition, for every given positive integer k, we construct a nontrivial snark having at least k 5-circuits in every 2-factor.

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Bibliographic Details
Published in:Discrete mathematics 2012-07, Vol.312 (14), p.2131-2134
Main Authors: Lukot’ka, R., Máčajová, E., Mazák, J., Škoviera, M.
Format: Article
Language:English
Subjects:
2-factor
5-circuit
5-cycle
Circuit
Snark
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Summary:For every even integer n≥28 we construct a cyclically 4-edge-connected snark of order n which has girth 5 and contains a 5-circuit in every 2-factor. In addition, for every given positive integer k, we construct a nontrivial snark having at least k 5-circuits in every 2-factor.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2011.05.026