Skip to main content
SpringerLink
Log in

Max Leaf Spanning Tree

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2005; Estivill-Castro, Fellows, Langston, Rosamond

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...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

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

    Google Scholar 

  2. Bonsma P, Brueggemann T, Woeginger G (2003) A faster FPT algorithm for finding spanning trees with many leaves. In: Proceedings of MFCS 2003. Lecture notes in computer science, vol 2747. Springer, Berlin, pp 259–268

    Google Scholar 

  3. Downey RG, Fellows MR (1999) Parameterized complexity, Monographs in computer science. Springer, New York

    Book  MATH  Google Scholar 

  4. Dehne F, Fellows M, Langston M, Rosamond F, Stevens K (2005) An O(2O(k)n3) FPT algorithm for the undirected feedback vertex set problem. In: Proceedings COCOON 2005. Lecture notes in computer science, vol 3595. Springer, Berlin, pp 859–869

    Google Scholar 

  5. Diaz-Gutierrez P, Bhushan A, Gopi M, Pajarola R (2006) Single-strips for fast interactive rendering. J Vis Comput 22(6):372–386

    Article  Google Scholar 

  6. Dutta R, Savage C (2005) 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, Nov 2005, pp 23–31. ISBN: 0-9716253-3-6. American Telecommunication Systems Management Association, Nashville

    Google Scholar 

  7. Egecioglu O, Gonzalez T (2001) Minimum-energy broadcast in simple graphs with limited node power. In: Proceedings of the IASTED international conference on parallel and distributed computing and systems (PDCS), Anaheim, Aug 2001, pp 334–338

    Google Scholar 

  8. Estivill-Castro V, Fellows MR, Langston MA, Rosamond FA (2005) FPT is P-time extremal structure I. In: Algorithms and complexity in Durham 2005. Texts in algorithmics, vol 4. Kings College Publications, London, pp 1–41

    Google Scholar 

  9. Fellows M, Langston M (1992) On well-partial-order theory and its applications to combinatorial problems of VLSI design. SIAM J Discret Math 5:117–126

    Article  MathSciNet  MATH  Google Scholar 

  10. Fellows M (2003) Blow-ups, win/win's and crown rules: some new directions in FPT. In: Proceedings of the 29th workshop on graph theoretic concepts in computer science (WG 2003). Lecture notes in computer science, vol 2880. Springer, Berlin, pp 1–12

    Google Scholar 

  11. Fellows M, McCartin C, Rosamond F, Stege U (2000) 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, vol 1974. Springer, Berlin, pp 240–251

    Google Scholar 

  12. Kleitman DJ, West DB (1991) Spanning trees with many leaves. SIAM J Discret Math 4:99–106

    Article  MathSciNet  MATH  Google Scholar 

  13. Kouider M, Vestergaard PD (2006) Generalized connected domination in graphs. Discret Math Theory Comput Sci (DMTCS) 8:57–64

    MathSciNet  MATH  Google Scholar 

  14. Lu H-I, Ravi R (1998) Approximating maximum leaf spanning trees in almost linear time. J Algorithm 29:132–141

    Article  MathSciNet  MATH  Google Scholar 

  15. Niedermeier R (2006) Invitation to fixed parameter algorithms. Lecture series in mathematics and its applications. Oxford University Press, Oxford

    Book  Google Scholar 

  16. Prieto-Rodriguez E (2005) Systematic kernelization in FPT algorithm design. Dissertation, School of Electrical Engineering and Computer Science, University of Newcastle

    Google Scholar 

  17. Solis-Oba R (1998) 2-approximation algorithm for finding a spanning tree with the maximum number of leaves. In: Proceedings of the 6th annual European symposium on algorithms (ESA'98). Lecture notes in computer science, vol 1461. Springer, Berlin, pp 441–452

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Frances Rosamond

Authors
  1. Frances Rosamond
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Rosamond, F. (2016). Max Leaf Spanning Tree. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_228

Download citation

Publish with us

Policies and ethics

Search

Navigation