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

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 1 |

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### Keywords

- 2-factor
- forbidden subgraph

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

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

**Pairs and triples of forbidden subgraphs and the existence of a 2-factor.** / Aldred, R. E.L.; Fujisawa, Jun; Saito, Akira.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 90, no. 1, pp. 61-82. https://doi.org/10.1002/jgt.22368

}

TY - JOUR

T1 - Pairs and triples of forbidden subgraphs and the existence of a 2-factor

AU - Aldred, R. E.L.

AU - Fujisawa, Jun

AU - Saito, Akira

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - 2-factor

KW - forbidden subgraph

UR - http://www.scopus.com/inward/record.url?scp=85056425436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056425436&partnerID=8YFLogxK

U2 - 10.1002/jgt.22368

DO - 10.1002/jgt.22368

M3 - Article

VL - 90

SP - 61

EP - 82

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -