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    Complexity of graph polynomials

    Noble, Steven (2007) Complexity of graph polynomials. In: McDiarmid, C.J.H. and Grimmett, G.R. (eds.) Combinatorics, Complexity and Chance: A Tribute to Dominic Welsh. Oxford, UK: Oxford University Press. ISBN 9780198571278.

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    This chapter examines the complexity of evaluating graph polynomials, related to the Tutte polynomial, for various classes of matroids. It begins with a short introduction to matroids, complexity, and the Tutte polynomial. The intractability results for the Tutte polynomial are then discussed, including proof of the most often quoted result of classifying the hard points for evaluation of the Tutte polynomial in the graphic case. Contrasting results are presented, giving polynomial time algorithms for restricted classes of input, particularly graphs with bounded tree-width. Finally, the complexity results for various classes of matroids are presented.


    Item Type: Book Section
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hall
    Date Deposited: 20 Jul 2020 11:34
    Last Modified: 09 Aug 2023 12:48


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