### Abstract

Kaiser and Vrana [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.

Original language | English |
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Pages (from-to) | 541-546 |

Number of pages | 6 |

Journal | Acta Mathematica Universitatis Comenianae |

Volume | 88 |

Issue number | 3 |

Publication status | Published - 2019 Sep 2 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

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.