The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
On a relation between graph edit distance and maximum common subgraph
Pattern Recognition Letters
Error Correcting Graph Matching: On the Influence of the Underlying Cost Function
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A study of graph spectra for comparing graphs and trees
Pattern Recognition
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Isomorphism for graphs of bounded feedback vertex set number
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Parameterized Complexity
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For similarity measures of labeled and unlabeled graphs, we study the complexity of the graph isomorphism problem for pairs of input graphs which are close with respect to the measure. More precisely, we show that for every fixed integer k we can decide in quadratic time whether a labeled graph G can be obtained from another labeled graph H by relabeling at most k vertices. We extend the algorithm solving this problem to an algorithm determining the number l of vertices that must be deleted and the number k of vertices that must be relabeled in order to make the graphs equivalent. The algorithm is fixed-parameter tractable in k + l. Contrasting these tractability results, we also show that for those similarity measures that change only by finite amount d whenever one edge is relocated, the problem of deciding isomorphism of input pairs of bounded distance d is equivalent to solving graph isomorphism in general.