Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
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
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
Tree-width for first order formulae
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
LIFO-search on digraphs: a searching game for cycle-rank
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
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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In [T. Johnson, N. Robertson, P.D. Seymour, R. Thomas, Directed tree-width, J. Combin. Theory Ser. B 82 (2001) 138-154] Johnson, Robertson, Seymour and Thomas define the notion of directed tree-width, dtw(D), of a directed graph D. They ask whether dtw(D)=k-1 implies that D has a haven of order k. A negative answer is given. Furthermore they define a generalisation of the robber and cops game of [P.D. Seymour, R. Thomas, Graph searching and a min-max theorem for tree-width, J. Combin. Theory Ser. B 58 (1993) 22-33] to digraphs. They ask whether it is true that if k cops can catch the robber on a digraph, then they can do so robber-monotonely. Again a negative answer is given. We also show that contraction of butterfly edges can increase directed tree-width.