### 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 |
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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 1 |

### Keywords

- Forbidden subgraph
- Near-perfect matching
- Perfect matching

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

*Journal of Combinatorial Theory. Series B*,

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