### Abstract

In this paper we give a sharp minimum degree condition for a 2-connected star-free graph to have a 2-factor containing specified edges. Let G be a 2-connected K _{1,n}-free graph with minimum degree n + d and I ⊂ E(G). If one of the followings holds, then G has a 2-factor which contains every edge in I: i) n = 3, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 8 if |I| = 2; ii) n = 4, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 11 if |I| = 2; iii) n ≥ 5, d ≥ 1 and |I| ≤ 1; iv) n ≥ 5, d ≥ [(√4n - 3 + l)/2] and |I| ≤ 2.

Original language | English |
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Pages (from-to) | 203-218 |

Number of pages | 16 |

Journal | SUT Journal of Mathematics |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2008 Dec 1 |

Externally published | Yes |

### Keywords

- 2-factor
- Minimum degree condition
- Star-free graphs

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Fourtounelli, O., Fujisawa, J., & Katerinis, P. (2008). On 2-factors in star-free graphs.

*SUT Journal of Mathematics*,*44*(2), 203-218.