Abstract
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 k such that a simple combinatorial algorithm, namely "the k-dimensional Weisfeiler--Lehman algorithm," decides isomorphism of graphs in C in polynomial time.
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Index Terms
- From polynomial time queries to graph structure theory
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From polynomial time queries to graph structure theory
ICDT '10: Proceedings of the 13th International Conference on Database TheoryIn a fundamental article on query languages for relational databases, Chandra and Harel [2] asked in 1982 whether there is a language that expresses precisely those queries which can be answered in polynomial time. Gurevich [10] later rephrased the ...
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