### Abstract

This paper considers the problem of finding a minimum-cardinality set of edges for a given k-connected graph whose addition makes it (k + 1)-connected. We give sharp lower and upper bounds for this minimum, where the gap between them is at most k - 2. This result is a generalization of the solved cases k = 1, 2, where the exact min-max formula is known. We present a polynomial-time approximation algorithm which makes a k-connected graph (k + 1)-connected by adding a new set of edges with size at most k - 2 over the optimum.

Original language | English |
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Pages (from-to) | 8-20 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 63 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1995 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics