New Results on the Complexity of Oriented Colouring on Restricted Digraph Classes
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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
A polynomial time algorithm for bounded directed pathwidth
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On the algorithmic effectiveness of digraph decompositions and complexity measures
Discrete Optimization
LIFO-search: A min-max theorem and a searching game for cycle-rank and tree-depth
Discrete Applied Mathematics
Hypertree-depth and minors in hypergraphs
Theoretical Computer Science
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
On tractable parameterizations of graph isomorphism
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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In contrast to undirected width measures (such as tree-width or clique-width), which have provided many important algorithmic applications, analogous measures for digraphs such as DAG-width or Kelly-width do not seem so successful. Several recent papers, e.g. those of Kreutzer---Ordyniak, Dankelmann---Gutin---Kim, or Lampis---Kaouri---Mitsou, have given some evidence for this. We support this direction by showing that many quite different problems remain hard even on graph classes that are restricted very beyond simply having small DAG-width. To this end, we introduce new measures K-width and DAG-depth. On the positive side, we also note that taking Kanté's directed generalization of rank-width as a parameter makes many problems fixed parameter tractable.