### 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 |
---|---|

Pages (from-to) | 160-207 |

Number of pages | 48 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 12 |

Issue number | 2 |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*SIAM Journal on Discrete Mathematics*,

*12*(2), 160-207.

**Edge-connectivity augmentation with partition constraints.** / Bang-Jensen, Jørgen; Gabow, Harold N.; Jordán, T.; Szigeti, Zoltán.

Research output: Contribution to journal › Article

*SIAM Journal on Discrete Mathematics*, vol. 12, no. 2, pp. 160-207.

}

TY - JOUR

T1 - Edge-connectivity augmentation with partition constraints

AU - Bang-Jensen, Jørgen

AU - Gabow, Harold N.

AU - Jordán, T.

AU - Szigeti, Zoltán

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032624453&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032624453

VL - 12

SP - 160

EP - 207

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -