Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Parallel tree contraction part 2: further applications
SIAM Journal on Computing
A logspace algorithm for tree canonization (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Isomorphism testing for embeddable graphs through definability
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Flexibility of polyhedral embeddings of graphs in surfaces
Journal of Combinatorial Theory Series B
Testing Isomorphism of Outerplanar Graphs in Parallel
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
Isomorphism for graphs embeddable on the projective plane
STOC '80 Proceedings of the twelfth 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
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
On isomorphism and canonization of tournaments and hypertournaments
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
Graphs of bounded treewidth can be canonized in AC1
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
The isomorphism problem for k-trees is complete for logspace
Information and Computation
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
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A function f of a graph is called a complete graph invariant if two given graphs G and H are isomorphic exactly when f(G) = f(H). If additionally, f(G) is a graph isomorphic to G, then f is called a canonical form for graphs. Gurevich [9] proves that any polynomial-time computable complete invariant can be transformed into a polynomial-time computable canonical form. We extend this equivalence to the polylogarithmic-time model of parallel computation for classes of graphs having either bounded rigidity index or small separators. In particular, our results apply to three representative classes of graphs embeddable into a fixed surface, namely, to 3-connected graphs admitting either a polyhedral or a large-edge-width embedding as well as to all embeddable 5-connected graphs. Another application covers graphs with treewidth bounded by a constant k. Since for the latter class of graphs a complete invariant is computable in NC, it follows that graphs of bounded treewidth have a canonical form (and even a canonical labeling) computable in NC.