Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
Five-coloring graphs on the torus
Journal of Combinatorial Theory Series B
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Finding and counting small induced subgraphs efficiently
Information Processing Letters
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Dynamic Representation of Sparse Graphs
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
On the complexity of fixed parameter clique and dominating set
Theoretical Computer Science
Linear time low tree-width partitions and algorithmic consequences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
The h-Index of a Graph and Its Application to Dynamic Subgraph Statistics
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Algorithms for Classes of Graphs with Bounded Expansion
Graph-Theoretic Concepts in Computer Science
Deciding First-Order Properties for Sparse Graphs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Extended dynamic subgraph statistics using h-index parameterized data structures
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Characterisations and examples of graph classes with bounded expansion
European Journal of Combinatorics
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We present a dynamic data structure representing a graph G, which allows addition and removal of edges from G and can determine the number of appearances of a graph of a bounded size as an induced subgraph of G. The queries are answered in constant time. When the data structure is used to represent graphs from a class with bounded expansion (which includes planar graphs and more generally all proper classes closed on topological minors, as well as many other natural classes of graphs with bounded average degree), the amortized time complexity of updates is polylogarithmic.