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A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5344))

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Abstract

We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter x(G), and construct a tree with at least (n − x(G) + 4)/3 leaves, and prove that no tree with more than (n − x(G) + 2)/2 leaves exists. In contrast to previous approximation algorithms for MaxLeaf, our algorithm works with connected dominating sets instead of constructing a tree directly. The algorithm also yields a 4/3-approximation for Minimum Connected Dominating Set in cubic graphs.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Paul Bonsma & Florian Zickfeld

Authors
  1. Paul Bonsma
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  2. Florian Zickfeld
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Editors and Affiliations

  1. Department of Computer Science, Durham University, South Road, DH1 3LE, Durham, UK

    Hajo Broersma , Tom Friedetzky  & Daniel Paulusma ,  & 

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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Bonsma, P., Zickfeld, F. (2008). A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2008. Lecture Notes in Computer Science, vol 5344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92248-3_7

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  • DOI: https://doi.org/10.1007/978-3-540-92248-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92247-6

  • Online ISBN: 978-3-540-92248-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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