### Abstract

Let F be a family of connected graphs. A graph G is said to be F-free if G is H-free for every graph H in F. We study the problem of characterizing the families of graphs F such that every large enough connected F-free graph of even order has a perfect matching. This problems was previously studied in Plummer and Saito (J Graph Theory 50(1):1-12, 2005), Fujita et al. (J Combin Theory Ser B 96(3):315-324, 2006) and Ota et al. (J Graph Theory, 67(3):250-259, 2011), where the authors were able to characterize such graph families F restricted to the cases {pipe}F{pipe} ≤ 1, {pipe}F{pipe} ≤ 2 and ≤ 3, respectively. In this paper, we complete the characterization of all the families that satisfy the above mentioned property. Additionally, we show the families that one gets when adding the condition {pipe}F{pipe} ≤ k for some k ≥ 4.

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

Pages (from-to) | 289-299 |

Number of pages | 11 |

Journal | Graphs and Combinatorics |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

- Forbidden subgraph
- Perfect matching

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Graphs and Combinatorics*,

*29*(2), 289-299. https://doi.org/10.1007/s00373-011-1102-6

**Forbidden Induced Subgraphs for Perfect Matchings.** / Ota, Katsuhiro; Sueiro, Gabriel.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 29, no. 2, pp. 289-299. https://doi.org/10.1007/s00373-011-1102-6

}

TY - JOUR

T1 - Forbidden Induced Subgraphs for Perfect Matchings

AU - Ota, Katsuhiro

AU - Sueiro, Gabriel

PY - 2013

Y1 - 2013

N2 - Let F be a family of connected graphs. A graph G is said to be F-free if G is H-free for every graph H in F. We study the problem of characterizing the families of graphs F such that every large enough connected F-free graph of even order has a perfect matching. This problems was previously studied in Plummer and Saito (J Graph Theory 50(1):1-12, 2005), Fujita et al. (J Combin Theory Ser B 96(3):315-324, 2006) and Ota et al. (J Graph Theory, 67(3):250-259, 2011), where the authors were able to characterize such graph families F restricted to the cases {pipe}F{pipe} ≤ 1, {pipe}F{pipe} ≤ 2 and ≤ 3, respectively. In this paper, we complete the characterization of all the families that satisfy the above mentioned property. Additionally, we show the families that one gets when adding the condition {pipe}F{pipe} ≤ k for some k ≥ 4.

AB - Let F be a family of connected graphs. A graph G is said to be F-free if G is H-free for every graph H in F. We study the problem of characterizing the families of graphs F such that every large enough connected F-free graph of even order has a perfect matching. This problems was previously studied in Plummer and Saito (J Graph Theory 50(1):1-12, 2005), Fujita et al. (J Combin Theory Ser B 96(3):315-324, 2006) and Ota et al. (J Graph Theory, 67(3):250-259, 2011), where the authors were able to characterize such graph families F restricted to the cases {pipe}F{pipe} ≤ 1, {pipe}F{pipe} ≤ 2 and ≤ 3, respectively. In this paper, we complete the characterization of all the families that satisfy the above mentioned property. Additionally, we show the families that one gets when adding the condition {pipe}F{pipe} ≤ k for some k ≥ 4.

KW - Forbidden subgraph

KW - Perfect matching

UR - http://www.scopus.com/inward/record.url?scp=84874651758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874651758&partnerID=8YFLogxK

U2 - 10.1007/s00373-011-1102-6

DO - 10.1007/s00373-011-1102-6

M3 - Article

AN - SCOPUS:84874651758

VL - 29

SP - 289

EP - 299

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 2

ER -