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Max Leaf Spanning Tree

2005; Estivill-Castro, Fellows, Langston, Rosamond

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Encyclopedia of Algorithms

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Keywords and Synonyms

Maximum leaf spanning tree; Connected dominating set; Extremal structure

Problem Definition

The Max Leaf Spanning Tree problem asks us to find a spanning tree with at least k leaves in an undirected graph. The decision version of parameterized Max Leaf Spanning Tree is the following:

MAX LEAF SPANNING TREE

Input: A connected graph G, and an integer k.

Parameter: An integer k.

Question: Does G have a spanning tree with at least k leaves?

The parameterized complexity of the nondeterministic polynomial‐time complete Max Leaf Spanning Tree problem has been extensively studied [2,3,9,11] using a variety of kernelization, branching and other fixed‐parameter tractable (FPT) techniques. The authors are the first to propose an extremal structure method for hard computational problems. The method, following in the sense of Grothendieck and in the spirit of the graph minors project of Robertson and Seymour, is that a mathematical project should unfold as a series of small...

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Recommended Reading

  1. Bonsma, P.: Spanning trees with many leaves: new extremal results and an improved FPT algorithm. Memorandum Department of Applied Mathematics, vol. 1793, University of Twente, Enschede (2006)

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  3. Downey, R.G., Fellows, M.R.: Parameterized complexity. Monographs in Computer Science. Springer, New York (1999)

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  4. Dehne, F., Fellows, M., Langston, M., Rosamond, F., Stevens, K.: An \( { O(2^{O(k)}n^{3}) } \) FPT algorithm for the undirected feedback vertex set problem. Proceedings COCOON 2005. Lecture Notes in Computer Science, vol. 3595, pp. 859–869. Springer, Berlin (2005)

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  6. Dutta, R., Savage, C.: A Note on the Complexity of Converter Placement Supporting Broadcast in WDM Optical Networks. In: Proceedings of the International Conference on Telecommunication Systems‐Modeling and Analysis, Dallas, November 2005 ISBN: 0-9716253-3-6 pp. 23–31. American Telecommunication Systems Management Association, Nashville

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  11. Fellows, M., McCartin, C., Rosamond, F., Stege, U.: Coordinatized kernels and catalytic reductions: an improved FPT algorithm for max leaf spanning tree and other problems. In: Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science (FST-TCS 2000). Lecture Notes in Theoretical Computer Science 1974, pp. 240–251. Springer, Berlin (2000)

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Author information

Authors and Affiliations

  1. Parameterized Complexity Research Unit, University of Newcastle, Callaghan, NSW, Australia

    Frances Rosamond

Authors
  1. Frances Rosamond
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Rosamond, F. (2008). Max Leaf Spanning Tree. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_228

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