Tight bounds and a fast FPT algorithm for directed Max-Leaf Spanning Tree
ACM Transactions on Algorithms (TALG)
Max-leaves spanning tree is APX-hard for cubic graphs
Journal of Discrete Algorithms
A faster exact algorithm for the directed maximum leaf spanning tree problem
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Kernelization for maximum leaf spanning tree with positive vertex weights
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Approximation algorithms for the maximum leaf spanning tree problem on acyclic digraphs
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem
Journal of Discrete Algorithms
On the directed Full Degree Spanning Tree problem
Discrete Optimization
A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs
SIAM Journal on Discrete Mathematics
Kernel(s) for problems with no kernel: On out-trees with many leaves
ACM Transactions on Algorithms (TALG)
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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The ROOTED MAXIMUM LEAF OUTBRANCHING problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at least k leaves. We use the notion of s 驴 t numbering studied in [19,6,20] to exhibit combinatorial bounds on the existence of spanning directed trees with many leaves. These combinatorial bounds allow us to produce a constant factor approximation algorithm for finding directed trees with many leaves, whereas the best known approximation algorithm has a $\sqrt{OPT}$-factor [11]. We also show that ROOTED MAXIMUM LEAF OUTBRANCHING admits an edge-quadratic kernel, improving over the vertex-cubic kernel given by Fernau et al [13].