A separator theorem for graphs of bounded genus
Journal of Algorithms
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
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
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
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth 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
Linear time low tree-width partitions and algorithmic consequences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
On forbidden subdivision characterizations of graph classes
European Journal of Combinatorics
Coloring triangle-free graphs on surfaces
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Small graph classes and bounded expansion
Journal of Combinatorial Theory Series B
Rank-width and tree-width of H-minor-free graphs
European Journal of Combinatorics
European Journal of Combinatorics
European Journal of Combinatorics
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Characterisations and examples of graph classes with bounded expansion
European Journal of Combinatorics
Forbidden graphs for tree-depth
European Journal of Combinatorics
Parameterized complexity of generalized domination problems
Discrete Applied Mathematics
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
Hypertree-depth and minors in hypergraphs
Theoretical Computer Science
Enumeration of first-order queries on classes of structures with bounded expansion
Proceedings of the 32nd symposium on Principles of database systems
Testing first-order properties for subclasses of sparse graphs
Journal of the ACM (JACM)
FO model checking of interval graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Distance-two coloring of sparse graphs
European Journal of Combinatorics
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Classes of graphs with bounded expansion have been introduced in [J. Nesetril, P. Ossona de Mendez, The grad of a graph and classes with bounded expansion, in: A. Raspaud, O. Delmas (Eds.), 7th International Colloquium on Graph Theory, in: Electronic Notes in Discrete Mathematics, vol. 22, Elsevier (2005), pp. 101-106; J. Nesetril, P. Ossona de Mendez, Grad and classes with bounded expansion I. Decompositions, European Journal of Combinatorics (2005) (submitted for publication)]. They generalize classes with forbidden topological minors (i.e. classes of graphs having no subgraph isomorphic to the subdivision of some graph in a forbidden family), and hence 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) [J. Nesetril, P. Ossona de Mendez, Grad and classes with bounded expansion I. Decompositions, European Journal of Combinatorics (2005) (submitted for publication)] (actually, of tree-depth [J. Nesetril, P. Ossona de Mendez, Tree depth, subgraph coloring and homomorphism bounds, European Journal of Combinatorics 27 (6) (2006) 1022-1041] at most i, which is sensibly stronger). Such partitions are central to the resolution of homomorphism problems like restricted homomorphism dualities [J. Nesetril, P. Ossona de Mendez, Grad and classes with bounded expansion III. Restricted dualities, European Journal of Combinatorics (2005) (submitted for publication)]. We give here a simple algorithm for computing 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 @f be a first-order logic sentence. We prove that any fixed graph property of type may be decided in linear time for input graphs in a fixed class with bounded expansion. We also show that for fixed p, computing the distances between two vertices up to distance p may be performed in constant time per query after a linear time preprocessing. Also, extending several earlier results, we show that a class of graphs has sublinear separators if it has sub-exponential expansion. This result is best possible in general.