Weighted interlace polynomials

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Weighted interlace polynomials

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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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