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Parameterized Algorithms for Directed Maximum Leaf Problems

  • Noga Alon
  • Fedor V. Fomin
  • Gregory Gutin
  • Michael Krivelevich
  • Saket Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

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.

Keywords

Span Tree Undirected Graph Tree Decomposition Oriented Graph Span Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Noga Alon
    • 1
  • Fedor V. Fomin
    • 2
  • Gregory Gutin
    • 3
  • Michael Krivelevich
    • 1
  • Saket Saurabh
    • 2
    • 4
  1. 1.Department of Mathematics, Tel Aviv University, Tel Aviv 69978Israel
  2. 2.Department of Informatics, University of Bergen, POB 7803, 5020 BergenNorway
  3. 3.Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EXUK
  4. 4.The Institute of Mathematical Sciences, Chennai, 600 017, Email: saket@imsc.res.inIndia

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