### Abstract

In [3], Faudree et al. considered the proposition “Every (X, Y)-free graph of sufficiently large order has a 2-factor,” and they determined those pairs (X, Y) which make this proposition true. Their result says that one of them is (X, Y) = (K_{1,4}, P_{4}). In this paper, we investigate the existence of 2-factors in r-connected (K_{1, k}, P_{4})-free graphs. We prove that if r ≥ 1 and k ≥ 2, and if G is an r-connected (K_{1, k}, P_{4})-free graph with minimum degree at least k − 1, then G has a 2-factor with at most max(k − r, 1) components unless (k − 1)K_{2} + (k − 2)K_{1} ⊆ G ⊆ (k − 1)K_{2} + K_{k−2}. The bound on the minimum degree is best possible.

Original language | English |
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Pages (from-to) | 415-420 |

Number of pages | 6 |

Journal | Tokyo Journal of Mathematics |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Jan 1 |

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### Keywords

- 2-factor
- Forbidden subgraph
- Minimum degree

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{1, k}, P

_{4})-Free Graphs.

*Tokyo Journal of Mathematics*,

*31*(2), 415-420. https://doi.org/10.3836/tjm/1233844061