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Title: The equivalence of two graph polynomials and a symmetric function
Authors: Merino, C
Noble, SD
Keywords: Graph polynomial;Graph symmetric function;Chromatic polynomial;Tutte polynomial;Polychromate
Issue Date: 2009
Publisher: Cambridge University Press
Citation: Combinatorics, Probability and Computing. 18 : 601-615
Abstract: The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any other. The definition of each of these functions suggests a natural way in which to strengthen them which also captures Tutte's universal V-function as a specialization. We show that the equivalence remains true for the strong functions thus answering a question raised by Dominic Welsh.
ISSN: 0963-5483
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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