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Universal Point Sets for Planar Three-Trees

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Algorithms and Data Structures (WADS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8037))

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Abstract

For every n ∈ ℕ, we present a set S n of O(n 5/3) points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of S n . This is the first subquadratic upper bound on the size of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.

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Author information

Authors and Affiliations

  1. Charles University, Prague, Czech Republic

    Radoslav Fulek

  2. California State University, Northridge, CA, USA

    Csaba D. Tóth

  3. University of Calgary, AB, Canada

    Csaba D. Tóth

Authors
  1. Radoslav Fulek
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  2. Csaba D. Tóth
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, ON, Canada

    Roberto Solis-Oba

  3. School of Computer Science, Carleton University, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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Fulek, R., Tóth, C.D. (2013). Universal Point Sets for Planar Three-Trees. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_30

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  • DOI: https://doi.org/10.1007/978-3-642-40104-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40103-9

  • Online ISBN: 978-3-642-40104-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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