### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 14 |

ISBN (Print) | 0169-2690 |

Publication status | Published - 1997 |

### Publication series

Name | Memorandum / University of Twente, Faculty of Applied Mathematics |
---|---|

Publisher | Universiteit Twente |

No. | 1372 |

### Keywords

- METIS-141163
- IR-30523

### Cite this

*Various results on the toughness of graphs*. (Memorandum / University of Twente, Faculty of Applied Mathematics; No. 1372). Enschede: Universiteit Twente.

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*Various results on the toughness of graphs*. Memorandum / University of Twente, Faculty of Applied Mathematics, no. 1372, Universiteit Twente, Enschede.

**Various results on the toughness of graphs.** / Broersma, Haitze J.; Engbers, E.A.; Trommel, H.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Various results on the toughness of graphs

AU - Broersma, Haitze J.

AU - Engbers, E.A.

AU - Trommel, H.

N1 - Memorandum fac. TW nr 1372

PY - 1997

Y1 - 1997

N2 - Let G be a graph, and let t 0 be a real number. Then G is t-tough if t!(G − S) jSj for all S V (G) with !(G − S) > 1, where !(G − S) denotes the number of components of G − S. The toughness of G, denoted by (G), is the maximum value of t for which G is t-tough (taking (Kn) = 1 for all n 1). G is minimally t-tough if (G) = t and (H) < t for every proper spanning subgraph H of G. We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sucient (degree) conditions implying (G) t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.

AB - Let G be a graph, and let t 0 be a real number. Then G is t-tough if t!(G − S) jSj for all S V (G) with !(G − S) > 1, where !(G − S) denotes the number of components of G − S. The toughness of G, denoted by (G), is the maximum value of t for which G is t-tough (taking (Kn) = 1 for all n 1). G is minimally t-tough if (G) = t and (H) < t for every proper spanning subgraph H of G. We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sucient (degree) conditions implying (G) t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.

KW - METIS-141163

KW - IR-30523

M3 - Report

SN - 0169-2690

T3 - Memorandum / University of Twente, Faculty of Applied Mathematics

BT - Various results on the toughness of graphs

PB - Universiteit Twente

CY - Enschede

ER -