### Abstract

Analogous pairs of theorems are investigated concerning coverings of directed and odd cuts. One such pair of results is the Lucchesi-Younger theorem on directed cuts and Seymour's theorem on odd cuts. The authors strengthen these results (incidentally providing a simple proof of Seymour's theorem). For example, the minimum cardinality of a T-join in a graph G equals (V,E) is proved to equal the maximum of SUMMATN q//T(V//i)/2 over all partitions of V where q//T(X) is the number of T-odd components of V minus X. Moreover, if G is bipartite, there is an optimal partition arising from a partition of the two parts. Secondly some orientation problems of undirected graphs are discussed. The results also emphasize the analogy between strong connectivity and parity conditions.

Original language | English |
---|---|

Pages (from-to) | 99-112 |

Number of pages | 14 |

Journal | Mathematical Programming Study |

Issue number | 22 |

Publication status | Published - Dec 1983 |

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Mathematical Programming Study*, (22), 99-112.

**COVERING DIRECTED AND ODD CUTS.** / Frank, A.; Tardos, Eva; Sebo, Andras.

Research output: Contribution to journal › Article

*Mathematical Programming Study*, no. 22, pp. 99-112.

}

TY - JOUR

T1 - COVERING DIRECTED AND ODD CUTS.

AU - Frank, A.

AU - Tardos, Eva

AU - Sebo, Andras

PY - 1983/12

Y1 - 1983/12

N2 - Analogous pairs of theorems are investigated concerning coverings of directed and odd cuts. One such pair of results is the Lucchesi-Younger theorem on directed cuts and Seymour's theorem on odd cuts. The authors strengthen these results (incidentally providing a simple proof of Seymour's theorem). For example, the minimum cardinality of a T-join in a graph G equals (V,E) is proved to equal the maximum of SUMMATN q//T(V//i)/2 over all partitions of V where q//T(X) is the number of T-odd components of V minus X. Moreover, if G is bipartite, there is an optimal partition arising from a partition of the two parts. Secondly some orientation problems of undirected graphs are discussed. The results also emphasize the analogy between strong connectivity and parity conditions.

AB - Analogous pairs of theorems are investigated concerning coverings of directed and odd cuts. One such pair of results is the Lucchesi-Younger theorem on directed cuts and Seymour's theorem on odd cuts. The authors strengthen these results (incidentally providing a simple proof of Seymour's theorem). For example, the minimum cardinality of a T-join in a graph G equals (V,E) is proved to equal the maximum of SUMMATN q//T(V//i)/2 over all partitions of V where q//T(X) is the number of T-odd components of V minus X. Moreover, if G is bipartite, there is an optimal partition arising from a partition of the two parts. Secondly some orientation problems of undirected graphs are discussed. The results also emphasize the analogy between strong connectivity and parity conditions.

UR - http://www.scopus.com/inward/record.url?scp=0020927336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020927336&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0020927336

SP - 99

EP - 112

JO - Mathematical Programming Study

JF - Mathematical Programming Study

SN - 0303-3929

IS - 22

ER -