### Abstract

A well-known theorem of Nash-Williams and Tutte gives a necessary and sufficient condition for the existence of k edge-disjoint spanning trees in an undirected graph. A corollary of this theorem is that every 2k-edge-connected graph has k edge-disjoint spanning trees. We show that the splitting-off theorem of Mader in undirected graphs implies a generalization of this to finding k edge-disjoint Steiner forests in Eulerian graphs. This leads to new 2-approximation rounding algorithms for certain constrained 0-1 forest problems considered by Goemans andWilliamson. These algorithms also produce approximate integer decompositions of fractional solutions. We then discuss open problems and outlets for this approach to the more general class of 0-1 skew supermodular network design problems.

Original language | English (US) |
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Pages (from-to) | 163-177 |

Number of pages | 15 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 23 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2008 |

### Keywords

- Approximation algorithm
- Integer decomposition
- Network design
- Supermodular function

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*SIAM Journal on Discrete Mathematics*,

*23*(1), 163-177. https://doi.org/10.1137/040617339