On 2-factors with a specified number of components in line graphs
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Abstract
Kaiser and Vr\’{a}na [European J. Combin. 33 (2012) 924--947] showed that every $5$-connected line graph of minimum degree at least $6$ is hamiltonian, which gives a partial solution to Thomassen's Conjecture on hamiltonicity of line graphs [J. Graph Theory 10 (1986) 309--324]. In this paper, we prove that every $5$-connected line graph of sufficiently large order compared with a given positive integer $k$ and of minimum degree at least $6$ also has a $2$-factor with exactly $k$ cycles. In order to show this result, we investigate minimum degree conditions for the existence of such a $2$-factor in hamiltonian line graphs.
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How to Cite
Chiba, S., Egawa, Y., Fujisawa, J., Saito, A., Schiermeyer, I., Tsugaki, M., & Yamashita, T.
(2019).
On 2-factors with a specified number of components in line graphs.
Acta Mathematica Universitatis Comenianae, 88(3), 541-546.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1251/732
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EUROCOMB 2019