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dc.contributor.author | Traldi, Lorenzo | |

dc.date.accessioned | 2011-01-06T14:44:42Z | |

dc.date.available | 2011-01-06T14:44:42Z | |

dc.date.issued | 2010-01 | |

dc.identifier.citation | Traldi, L. 2010 "Weighted interlace polynomials." Combinatorics, Probability and Computing 19 (1): 133-157. | en_US |

dc.identifier.uri | http://hdl.handle.net/10385/782 | |

dc.description.abstract | The interlace polynomials introduced by Arratia, Bollobas and Sorkin extend to invariants of graphs with vertex weights, and these weighted interlace polynomials have several novel properties. One novel property is a version of the fundamental three-term formula q(G) = q(G - a) + q(G(ab) - b) + ((x - 1)(2) - 1)q(G(ab) - a - b) that lacks the last term. It follows that interlace polynomial computations can be represented by binary trees rather than mixed binary-ternary trees. Binary computation trees provide a description of q(G) that is analogous to the activities description of the Tutte polynomial. If G is a tree or forest then these 'algorithmic activities' are associated with a certain kind of independent set in G. Three other novel properties are weighted pendant-twin reductions, which involve removing certain kinds of vertices from a graph and adjusting the weights of the remaining vertices in such a way that the interlace polynomials are unchanged. These reductions allow for smaller computation trees as they eliminate some branches. If a graph can be completely analysed using pendant-twin reductions, then its interlace polynomial can be calculated in polynomial time. An intuitively pleasing property is that graphs which can be constructed through graph substitutions have vertex-weighted interlace polynomials which can be obtained through algebraic substitutions. | en_US |

dc.publisher | Combinatorics, Probability and Computing | en_US |

dc.title | Weighted interlace polynomials | en_US |

dc.type | Article | en_US |

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