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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Parameterized Algorithms for Directed Maximum Leaf Problems
verfasst von : Noga Alon, Fedor V. Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
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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.