### Abstract

In the well-solved edge-connectivity augmentation problem, a minimum cardinality set F of edges to add to a given undirected graph to make it k-connected should be found. The generalization where every edge of F must go between two different sets of a given partition of the vertex set is solved. A special case of this partition-constrained problem increases the edge-connectivity of a bipartite graph to k while preserving bipartiteness. Based on this special case, an application of the results in statics is presented. The solution to the general partition-constrained problem gives a min-max formula for |F| which includes as a special case the original min-max formula for the problem without partition constraints.

Original language | English |
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Pages (from-to) | 160-207 |

Number of pages | 48 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 12 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1999 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*SIAM Journal on Discrete Mathematics*,

*12*(2), 160-207. https://doi.org/10.1137/S0895480197324700