Communication: On complexity of Minimum Leaf Out-Branching problem
Discrete Applied Mathematics
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Digraph decompositions and monotonicity in digraph searching
Theoretical 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
Journal of Combinatorial Optimization
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
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We place our focus on the gap between treewidth's success in producing fixed-parameter polynomial algorithms for hard graph problems, and specifically Hamiltonian Circuit and Max Cut, and the failure of its directed variants (directed tree-width [9], DAG-width [11] and kelly-width [8]) to replicate it in the realm of digraphs. We answer the question of why this gap exists by giving two hardness results: we show that Directed Hamiltonian Circuit is W[2]-hard when the parameter is the width of the input graph, for any of these widths, and that Max Di Cut remains NP-hard even when restricted to DAGs, which have the minimum possible width under all these definitions. Our results also apply to directed pathwidth.