Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Moderately Exponential Bound for Graph Isomorphism
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Isomorphism of graphs with bounded eigenvalue multiplicity
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
Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs
Discrete Applied Mathematics
Faster fixed parameter tractable algorithms for finding feedback vertex sets
ACM Transactions on Algorithms (TALG)
Computing Automorphism Groups of Chordal Graphs Whose Simplicial Components Are of Small Size
IEICE - Transactions on Information and Systems
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Improved algorithms for feedback vertex set problems
Journal of Computer and System Sciences
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
What Makes Equitable Connected Partition Easy
Parameterized and Exact Computation
Chordal deletion is fixed-parameter tractable
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Parameterized complexity of vertex deletion into perfect graph classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Isomorphism of (mis)labeled graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
On tractable parameterizations of graph isomorphism
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Graph isomorphism for graph classes characterized by two forbidden induced subgraphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Two-Layer Planarization parameterized by feedback edge set
Theoretical Computer Science
Parameterized complexity of vertex deletion into perfect graph classes
Theoretical Computer Science
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This paper presents an ${\mathcal O}(n^2)$ algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixed-parameter tractable with respect to the feedback vertex set number. Central to the algorithm is a new technique consisting of an application of reduction rules that produce an isomorphism-invariant outcome, interleaved with the creation of increasingly large partial isomorphisms.