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CORR

2007

Springer

2007

Springer

We deﬁne a multivariate polynomial that generalizes in a uniﬁed way the twovariable interlace polynomial deﬁned by Arratia, Bollob´as and Sorkin on the one hand, and a one-variable variant of it deﬁned by Aigner and van der Holst on the other. We determine a recursive deﬁnition for our polynomial that is based on local complementation and pivoting like the recursive deﬁnitions of Tutte’s polynomial and of its multivariate generalizations are based on edge deletions and contractions. We also show that bounded portions of our polynomial can be evaluated in polynomial time for graphs of bounded clique-width. Our proof uses an expression of the interlace polynomial in monadic second-order logic, and works actually for every polynomial expressed in monadic second-order logic in a similar way.

Related Content

Added |
13 Dec 2010 |

Updated |
13 Dec 2010 |

Type |
Journal |

Year |
2007 |

Where |
CORR |

Authors |
Bruno Courcelle |

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