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Parameterized Algorithms for Directed Maximum Leaf Problems

Noga Alon·Fedor Fomin·Gregory Gutin·Michael Krivelevich·Saket Saurabh
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Abstract

We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that includes all strong and acyclic digraphs. This settles completely an open question of Fellows and solves another one for digraphs in $\cal L$. Our algorithms are based on the following combinatorial result which can be viewed as a generalization of many results for a `spanning tree with many leaves' in the undirected case, and which is interesting on its own: If a digraph $D\in \cal L$ of order $n$ with minimum in-degree at least 3 contains a rooted spanning tree, then $D$ contains one with at least $(n/2)^{1/5}-1$ leaves.

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BibTeXRIS

Noga Alon, Fedor Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh. 2007-02-08. Parameterized Algorithms for Directed Maximum Leaf Problems. https://arxiv.org/abs/cs/0702049

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