Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
A logspace algorithm for tree canonization (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Journal of Algorithms
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Theoretical Computer Science
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Completeness results for graph isomorphism
Journal of Computer and System Sciences
Bounded Color Multiplicity Graph Isomorphism is in the #L Hierarchy
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Parallel algorithms for permutation groups and graph isomorphism
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Undirected connectivity in log-space
Journal of the ACM (JACM)
Planar Graph Isomorphism is in Log-Space
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The Isomorphism Problem for k-Trees Is Complete for Logspace
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Logspace Versions of the Theorems of Bodlaender and Courcelle
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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
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The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time. We give restricted space algorithms for these problems proving the following results:*Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be computed within logspace. *For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e. when only isomorphisms are considered, mapping bags in one decomposition blockwise onto bags in the other decomposition) is in L. *For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in LogCFL. *As a corollary the isomorphism problem for bounded treewidth graphs is in LogCFL. This improves the known TC^1 upper bound for the problem given by Grohe and Verbitsky.