### 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 |
---|---|

Pages (from-to) | 203-218 |

Number of pages | 16 |

Journal | SUT Journal of Mathematics |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*SUT Journal of Mathematics*,

*44*(2), 203-218.

**On 2-factors in star-free graphs.** / Fourtounelli, Olga; Fujisawa, Jun; Katerinis, P.

Research output: Contribution to journal › Article

*SUT Journal of Mathematics*, vol. 44, no. 2, pp. 203-218.

}

TY - JOUR

T1 - On 2-factors in star-free graphs

AU - Fourtounelli, Olga

AU - Fujisawa, Jun

AU - Katerinis, P.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - 2-factor

KW - Minimum degree condition

KW - Star-free graphs

UR - http://www.scopus.com/inward/record.url?scp=84857705938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857705938&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84857705938

VL - 44

SP - 203

EP - 218

JO - SUT Journal of Mathematics

JF - SUT Journal of Mathematics

SN - 0916-5746

IS - 2

ER -