### Abstract

Let H be a set of connected graphs, each of which has order at least three, and suppose that there exist infinitely many connected H-free graphs of minimum degree at least two and all except for finitely many of them have a 2-factor. In [J. Graph Theory, 64 (2010), 250–266], we proved that if |H| ≤ 3, then one of the members in H is a star. In this article, we determine the remaining members of H and hence give a complete characterization of the pairs and triples of forbidden subgraphs.

Original language | English |
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Pages (from-to) | 61-82 |

Number of pages | 22 |

Journal | Journal of Graph Theory |

Volume | 90 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 Jan |

### Keywords

- 2-factor
- forbidden subgraph

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Aldred, R. E. L., Fujisawa, J., & Saito, A. (2019). Pairs and triples of forbidden subgraphs and the existence of a 2-factor.

*Journal of Graph Theory*,*90*(1), 61-82. https://doi.org/10.1002/jgt.22368