Monotonicity in graph searching
Journal of Algorithms
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
An Algorithm for Finding a Minimum Equivalent Graph of a Digraph
Journal of the ACM (JACM)
Journal of Combinatorial Theory Series B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
On the monotonicity of games generated by symmetric submodular functions
Discrete Applied Mathematics - Submodularity
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Monotonicity of non-deterministic graph searching
Theoretical Computer Science
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Digraph Strong Searching: Monotonicity and Complexity
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
Searching for a Visible, Lazy Fugitive
Graph-Theoretic Concepts in Computer Science
On the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
On Digraph Width Measures in Parameterized Algorithmics
Parameterized and Exact Computation
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
D-Width: a more natural measure for directed tree width
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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Graph decompositions such as tree-decompositions and associated width measures have been the focus of much attention in structural and algorithmic graph theory. In particular, it has been found that many otherwise intractable problems become tractable on graph classes of bounded tree-width. More recently, proposals have been made to define a similar notion to tree-width for directed graphs. Several proposals have appeared so far, supported by algorithmic applications. In this paper we explore the limits of algorithmic applicability of digraph decompositions and show that various natural candidates for problems, which potentially could benefit from digraphs having small ''directed width'', remain NP-complete even on almost acyclic graphs. Closely related to graph and digraph decompositions are graph searching games. An important property of graph searching games is monotonicity and a large number of papers addresses the question whether particular variants of these games are monotone. However, so far for two natural types of graph searching games-underlying DAG- and Kelly-decompositions-the question whether they are monotone was still open. We settle this issue by showing that both variants, the visible and the inert invisible graph searching games on directed graphs, are non-monotone.