Optimal node ranking of trees in linear time
Information Processing Letters
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Regular Article: Bi-complement Reducible Graphs
Advances in Applied Mathematics
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
The Complexity of First-Order and Monadic Second-Order Logic Revisited
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
Algorithmic meta-theorems for restrictions of treewidth
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Sparsity: Graphs, Structures, and Algorithms
Sparsity: Graphs, Structures, and Algorithms
Twin-Cover: beyond vertex cover in parameterized algorithmics
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Model checking lower bounds for simple graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Recent characterization [9] of those graphs for which coloured MSO2 model checking is fast raised the interest in the graph invariant called tree-depth. Looking for a similar characterization for (coloured) MSO1, we introduce the notion of shrub-depth of a graph class. To prove that MSO1 model checking is fast for classes of bounded shrub-depth, we show that shrub-depth exactly characterizes the graph classes having interpretation in coloured trees of bounded height. We also introduce a common extension of cographs and of graphs with bounded shrub-depth -- m-partite cographs (still of bounded clique-width), which are well quasi-ordered by the relation "is an induced subgraph of" and therefore allow polynomial time testing of hereditary properties.