### 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 |

### Keywords

- forbidden subgraph
- toughness

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Ota, K., & Sueiro, G. (2013). Forbidden induced subgraphs for toughness.

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