Title | **On the universal Gröbner bases of toric ideals of graphs** |

Author(s) | Christos Tatakis, Apostolos Thoma |

Type | Article in Journal |

Abstract | The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis. |

Keywords | Toric ideals, Toric varieties, Graver basis, Graphs Universal Gröbner bases, Term orders |

ISSN | 0097-3165 |

URL |
http://www.sciencedirect.com/science/article/pii/S0097316511000069 |

Language | English |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 118 |

Number | 5 |

Pages | 1540 - 1548 |

Year | 2011 |

Edition | 0 |

Translation |
No |

Refereed |
No |