Optimal node ranking of trees in linear time
Information Processing Letters
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Journal of the ACM (JACM)
Geometric Separators for Finite-Element Meshes
SIAM Journal on Scientific Computing
Combinatorial aspects of geometric graphs
Computational Geometry: Theory and Applications
Subgraph isomorphism in planar graphs and related problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Finding Minimally Weighted Subgraphs
WG '90 Proceedings of the 16rd International Workshop on Graph-Theoretic Concepts in Computer Science
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
Grad and classes with bounded expansion II. Algorithmic aspects
European Journal of Combinatorics
Forbidden lifts (NP and CSP for combinatorialists)
European Journal of Combinatorics
Grad and classes with bounded expansion III. Restricted graph homomorphism dualities
European Journal of Combinatorics
Efficient First-Order Model-Checking Using Short Labels
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Coloring triangle-free graphs on surfaces
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Fraternal augmentations, arrangeability and linear Ramsey numbers
European Journal of Combinatorics
Small graph classes and bounded expansion
Journal of Combinatorial Theory Series B
Compact labelings for efficient first-order model-checking
Journal of Combinatorial Optimization
European Journal of Combinatorics
European Journal of Combinatorics
Characterisations and examples of graph classes with bounded expansion
European Journal of Combinatorics
Forbidden graphs for tree-depth
European Journal of Combinatorics
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
LIFO-search: A min-max theorem and a searching game for cycle-rank and tree-depth
Discrete Applied Mathematics
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
NP by means of lifts and shadows
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Testing first-order properties for subclasses of sparse graphs
Journal of the ACM (JACM)
A dynamic data structure for counting subgraphs in sparse graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
Distance-two coloring of sparse graphs
European Journal of Combinatorics
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Classes of graphs with bounded expansion have been introduced in [15], [12]. They generalize both proper minor closed classes and classes with bounded degree.For any class with bounded expansion C and any integer p there exists a constant N(C,p) so that the vertex set of any graph G ∈ C may be partitioned into at most N(C,p) parts, any i ≤ p parts of them induce a subgraph of tree-width at most (i-1) [12] (actually, of tree-depth [16] at most i, what is sensibly stronger). Such partitions are central to the resolution of homomorphism problems like restricted homomorphism dualities [14].We give here a simple algorithm to compute such partitions and prove that if we restrict the input graph to some fixed class C with bounded expansion, the running time of the algorithm is bounded by a linear function of the order of the graph (for fixed C and p).This result is applied to get a linear time algorithm for the subgraph isomorphism problem with fixed pattern and input graphs in a fixed class with bounded expansion.More generally, let φ be a first order logic sentence. We prove that any fixed graph property of type "∃X: (|X| ≤ p) ⇿(G[X]=φ)" may be decided in linear time for input graphs in a fixed class with bounded expansion.