From Polynomial Time Queries to Graph Structure Theory.

We give a logical characterization of the polynomial-time properties of graphs with excluded minors: For every class C of graphs such that some graph H is not a minor of any graph in C, a property P of graphs in C is decidable in polynomial time if and only if it is definable in fixed-point logic wi...

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Publicado en:Communications of the ACM Vol. 54; no. 6; pp. 104 - 113
Autor principal: Grohe, Martin
Formato: Artículo
Publicado: Association for Computing Machinery Jun2011
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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        atl: From Polynomial Time Queries to Graph Structure Theory.
      aug:
        au: Grohe, Martin
        affil: Humboldt-Universität Berlin, Germany.
      su:
        Polynomials
        Querying (Computer science)
        Graph theory
        Algorithms
        Set theory
        Computer programming
      sug:
        subj:
          Polynomials
          Querying (Computer science)
          Graph theory
          Algorithms
          Set theory
          Computer programming
      ab: We give a logical characterization of the polynomial-time properties of graphs with excluded minors: For every class C of graphs such that some graph H is not a minor of any graph in C, a property P of graphs in C is decidable in polynomial time if and only if it is definable in fixed-point logic with counting. Furthermore, we prove that for every class C of graphs with excluded minors there is a κ such that a simple combinatorial algorithm, namely "the κ-dimensional Weisfeiler--Lehman algorithm," decides isomorphism of graphs in C in polynomial time.
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      doctype: Article
      src: R
    language: English
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          year: 2011
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