# Publication: A counterexample to the dominating set conjecture

All || By Area || By YearTitle | A counterexample to the dominating set conjecture |
---|---|

Authors/Editors* | Antoine Deza, Gabriel Indik |

Where published* | Optimization Letters |

How published* | Journal |

Year* | 2007 |

Volume | 1 |

Number | 2 |

Pages | 163-169 |

Publisher | Springer |

Keywords | Dominating set conjecture - Metric polyhedra - Cut polyhedra |

Link | http://springerlink.metapress.com/content/h33km11w17493029/?p=d0f54ec05fce408e9fabd38fb75907c6&pi=0 |

Abstract |
The metric polytope met_n is the polyhedron associated with all semimetrics on n nodes and defined by the triangle inequalities x_ij â x_ik â x_jk â¤ 0 and x_ij + x_ik + x_jk â¤ 2 for all triples i, j, k of {1,..., n}. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n â¤ 8 and, in particular, for the 1,550,825,600 vertices of met_8. While the overwhelming majority of the known vertices of met_9 satisfy the conjecture, we exhibit a fractional vertex not adjacent to any integral vertex. |

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