Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
Two Short Proofs Concerning Tree-Decompositions
Combinatorics, Probability and Computing
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Digraph searching, directed vertex separation and directed pathwidth
Discrete Applied Mathematics
Monotonicity in digraph search problems
Theoretical Computer Science
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
Recognizing digraphs of Kelly-width 2
Discrete Applied Mathematics
Directed searching digraphs: monotonicity and complexity
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Characterization and recognition of digraphs of bounded Kelly-width
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Undirected graphs of entanglement 2
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Pure Nash equilibria: complete characterization of hard and easy graphical games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Digraph decompositions and monotonicity in digraph searching
Theoretical Computer Science
LIFO-search on digraphs: a searching game for cycle-rank
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Directed nowhere dense classes of graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A polynomial time algorithm for bounded directed pathwidth
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
The dag-width of directed graphs
Journal of Combinatorial Theory Series B
LIFO-search: A min-max theorem and a searching game for cycle-rank and tree-depth
Discrete Applied Mathematics
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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Due to extensive research on tree-width for undirected graphs and due to its many applications in various fields it has been a natural desire for many years to generalize the idea of tree decomposition to directed graphs, but since many parameters in tree-width behave very differently in the world of digraphs, the generalization is still in its preliminary steps. In this paper, after surveying the main work that has been done on this topic, we propose a new simple definition for directed tree-width and prove a special case of the min-max theorem (duality theorem) relating haven order, bramble number, and tree-width on digraphs. We also compare our definition with previous definitions and study the behavior of some tree-width like parameters such as brambles and havens on digraphs.