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  • It is a classical result of Jaeger, Vertigan and Welsh that evaluating the Tutte polynomial of a graph is $\#P$-hard in all but few special points. On the other hand, several papers in past years have shown that the Tutte polynomial of a graph can be efficiently computed for graphs of bounded tree-width. In this paper we present a recursive formula computing the Tutte polynomial of a matroid $\md M$ represented over a finite field (which includes all graphic matroids), using a so called parse tree of a branch-decomposition of $\md M$. This formula provides an algorithm computing the Tutte polynomial for a representable matroid of bounded branch-width in polynomial time with a fixed exponent.
  • It is a classical result of Jaeger, Vertigan and Welsh that evaluating the Tutte polynomial of a graph is $\#P$-hard in all but few special points. On the other hand, several papers in past years have shown that the Tutte polynomial of a graph can be efficiently computed for graphs of bounded tree-width. In this paper we present a recursive formula computing the Tutte polynomial of a matroid $\md M$ represented over a finite field (which includes all graphic matroids), using a so called parse tree of a branch-decomposition of $\md M$. This formula provides an algorithm computing the Tutte polynomial for a representable matroid of bounded branch-width in polynomial time with a fixed exponent. (en)
Title
  • The Tutte Polynomial for Matroids of Bounded Branch-Width
  • The Tutte Polynomial for Matroids of Bounded Branch-Width (en)
skos:prefLabel
  • The Tutte Polynomial for Matroids of Bounded Branch-Width
  • The Tutte Polynomial for Matroids of Bounded Branch-Width (en)
skos:notation
  • RIV/00216224:14330/06:00016574!RIV10-MSM-14330___
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  • P(1ET101940420), P(1M0545)
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  • 3
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  • 504558
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  • RIV/00216224:14330/06:00016574
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  • representable matroid; Tutte polynomial; branch-width (en)
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  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [A32DCDEF017B]
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  • Combin. Prob. Computing
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  • 15
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  • Hliněný, Petr
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  • 0963-5483
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  • 14330
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