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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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COMPLEXITY OF GRAPH POLYNOMIALS

COMPLEXITY OF GRAPH POLYNOMIALS

Chapter:
(p.191) 13 COMPLEXITY OF GRAPH POLYNOMIALS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Steven D. Noble

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0013

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.

Keywords:   graph polynomials, Tutte polynomial, matroids, graphs, polynomial time algorithms

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