### Abstract

The Generalized Minimum Spanning Tree problem denoted by GMST is a variant of the classical Minimum Spanning Tree problem in which nodes are partitioned into clusters and the problem calls for a minimum cost tree spanning at least one node from each cluster. A different version of the problem, called E-GMST arises when exactly one node from each cluster has to be visited. Both GMST problem and E-GMST problem are NP-hard problems. In this paper, we model GMST problem and E-GMST problem as integer linear programs and study the facial structure of the corresponding polytopes.

Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 9 |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1587 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C05
- MSC-90C11
- IR-65774
- MSC-90B10
- EWI-3407
- MSC-90C27

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## Cite this

Pop, P. C. (2001).

*The generalized minimum spanning tree polytope and related polytopes*. (Memorandum; No. 1587). Enschede: University of Twente, Department of Applied Mathematics.