A Two-Variable Interlace Polynomial
نویسندگان
چکیده
منابع مشابه
A multivariate interlace polynomial
We define a multivariate polynomial that generalizes several interlace polynomials defined by Arratia, Bollobas and Sorkin on the one hand, and Aigner and van der Holst on the other. We follow the route traced by Sokal, who defined a multivariate generalization of Tutte’s polynomial. We also show that bounded portions of our interlace polynomial can be evaluated in polynomial time for graphs of...
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Generalizing a previous one-variable " interlace polynomial " , we consider a new interlace polynomial in two variables. The polynomial can be computed in two very different ways. The first is an expansion analogous to the state space expansion of the Tutte polynomial; the differences are that our expansion is over vertex rather than edge subsets, the rank of the subset appears positively rathe...
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We relate the oneand two-variable interlace polynomials of a graph to the spectra of a quadratic boolean function with respect to a strategic subset of local unitary transforms. By so doing we establish links between graph theory, cryptography, coding theory, and quantum entanglement. We establish the form of the interlace polynomial for certain functions, provide new one and two-variable inter...
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We consider the two-variable interlace polynomial introduced by Arratia, Bollobás and Sorkin (2004). We develop two graph transformations which allow us to derive point-to-point reductions for the interlace polynomial. Exploiting these reductions we obtain new results concerning the computational complexity of evaluating the interlace polynomial at a fixed point. Regarding exact evaluation, we ...
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Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial. It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an ...
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ژورنال
عنوان ژورنال: COMBINATORICA
سال: 2004
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-004-0035-6