### Abstract

Let A(n, k, t) denote the smallest integer e for which every k-connected graph on n vertices can be made (k + t)-connected by adding e new edges. We determine A(n, k, t) for all values of n, k, and t in the case of (directed and undirected) edge-connectivity and also for directed vertex-connectivity. For undirected vertex-connectivity we determine A(n, k, 1) for all values of n and k. We also describe the graphs that attain the extremal values.

Original language | English |
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Pages (from-to) | 179-193 |

Number of pages | 15 |

Journal | Journal of Graph Theory |

Volume | 31 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 1999 |

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### Keywords

- Connectivity
- Directed graphs
- Edge-splitting
- Graph connectivity augmentation

### ASJC Scopus subject areas

- Geometry and Topology