Relational queries computable in polynomial time
Information and Control
Topological graph theory
The graph genus problem is NP-complete
Journal of Algorithms
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
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A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface
SIAM Journal on Discrete Mathematics
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Isomorphism testing for embeddable graphs through definability
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Upper bounds to the clique width of graphs
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Definability and Descriptive Complexity on Databases of Bounded Tree-Width
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Expressive Equivalence of Least and Inflationary Fixed-Point Logic
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Inductive Definability with Counting on Finite Structures
CSL '92 Selected Papers from the Workshop on Computer Science Logic
Moderately Exponential Bound for Graph Isomorphism
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
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STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational queries computable in polynomial time (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
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Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Planar graphs: logical complexity and parallel isomorphism tests
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
From invariants to canonization in parallel
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Fixed-Point Definability and Polynomial Time on Graphs with Excluded Minors
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Capturing Polynomial Time on Interval Graphs
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
From polynomial time queries to graph structure theory
Communications of the ACM
Testing graph isomorphism in parallel by playing a game
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Experiments with reduction finding
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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We give a logical characterization of the polynomial-time properties of graphs embeddable in some surface. For every surface S, a property P of graphs embeddable in S is decidable in polynomial time if and only if it is definable in fixed-point logic with counting. It is a consequence of this result that for every surface S there is a k such that a simple combinatorial algorithm, namely “the k-dimensional Weisfeiler-Lehman algorithm”, decides isomorphism of graphs embeddable in S in polynomial time. We also present (without proof) generalizations of these results to arbitrary classes of graphs with excluded minors.