### 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 relation between forbidden subgraphs in a connected graph G and the resulting toughness of G. In particular, we consider the problem of characterizing the graph families F such that every large enough connected F-free graph is t-tough. In this article, we solve this problem for every real positive number t.

Original language | English |
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Pages (from-to) | 191-202 |

Number of pages | 12 |

Journal | Journal of Graph Theory |

Volume | 73 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 Jun |

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### Keywords

- forbidden subgraph
- toughness

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*73*(2), 191-202. https://doi.org/10.1002/jgt.21667

**Forbidden induced subgraphs for toughness.** / Ota, Katsuhiro; Sueiro, Gabriel.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 73, no. 2, pp. 191-202. https://doi.org/10.1002/jgt.21667

}

TY - JOUR

T1 - Forbidden induced subgraphs for toughness

AU - Ota, Katsuhiro

AU - Sueiro, Gabriel

PY - 2013/6

Y1 - 2013/6

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 relation between forbidden subgraphs in a connected graph G and the resulting toughness of G. In particular, we consider the problem of characterizing the graph families F such that every large enough connected F-free graph is t-tough. In this article, we solve this problem for every real positive number t.

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 relation between forbidden subgraphs in a connected graph G and the resulting toughness of G. In particular, we consider the problem of characterizing the graph families F such that every large enough connected F-free graph is t-tough. In this article, we solve this problem for every real positive number t.

KW - forbidden subgraph

KW - toughness

UR - http://www.scopus.com/inward/record.url?scp=84875836932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875836932&partnerID=8YFLogxK

U2 - 10.1002/jgt.21667

DO - 10.1002/jgt.21667

M3 - Article

AN - SCOPUS:84875836932

VL - 73

SP - 191

EP - 202

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 2

ER -