Journal of Combinatorial Theory Series B
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
Spanning Directed Trees with Many Leaves
SIAM Journal on Discrete Mathematics
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Directed nowhere dense classes of graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the algorithmic effectiveness of digraph decompositions and complexity measures
Discrete Optimization
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in D an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree zero. Gutin, Razgon and Kim [G. Gutin, I. Razgon, E.J. Kim, Minimum leaf out-branching problems, in: Proc. 4th International Conference on Algorithmic Aspects in Information and Management, AAIM'08, in: Lect. Notes Comput. Sci., vol. 5034 2008, pp. 235-246] proved that MinLOB is polynomial time solvable for acyclic digraphs which are exactly the digraphs of directed path-width (DAG-width, directed tree-width, respectively) 0. We investigate how much one can extend this polynomiality result. We prove that already for digraphs of directed path-width (directed tree-width, DAG-width, respectively) 1, MinLOB is NP-hard. On the other hand, we show that for digraphs of restricted directed tree-width (directed path-width, DAG-width, respectively) and a fixed integer k, the problem of checking whether there is an out-branching with at most k leaves is polynomial time solvable.