### Abstract

In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases. (1)Every graph in H is triangle-free.(2) H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases.

Original language | English |
---|---|

Pages (from-to) | 315-324 |

Number of pages | 10 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 96 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 May |

### Fingerprint

### Keywords

- Forbidden subgraph
- Near-perfect matching
- Perfect matching

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*96*(3), 315-324. https://doi.org/10.1016/j.jctb.2005.08.002

**A pair of forbidden subgraphs and perfect matchings.** / Fujita, Shinya; Kawarabayashi, Ken ichi; Leonardo Lucchesi, Claudio; Ota, Katsuhiro; Plummer, Michael D.; Saito, Akira.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 96, no. 3, pp. 315-324. https://doi.org/10.1016/j.jctb.2005.08.002

}

TY - JOUR

T1 - A pair of forbidden subgraphs and perfect matchings

AU - Fujita, Shinya

AU - Kawarabayashi, Ken ichi

AU - Leonardo Lucchesi, Claudio

AU - Ota, Katsuhiro

AU - Plummer, Michael D.

AU - Saito, Akira

PY - 2006/5

Y1 - 2006/5

N2 - In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases. (1)Every graph in H is triangle-free.(2) H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases.

AB - In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases. (1)Every graph in H is triangle-free.(2) H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases.

KW - Forbidden subgraph

KW - Near-perfect matching

KW - Perfect matching

UR - http://www.scopus.com/inward/record.url?scp=33645931353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645931353&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2005.08.002

DO - 10.1016/j.jctb.2005.08.002

M3 - Article

VL - 96

SP - 315

EP - 324

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 3

ER -