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International Symposium on Algorithms and Computation

ISAAC 2002: Algorithms and Computation pp 416–427Cite as

Bounded-Degree Independent Sets in Planar Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

Abstract

An independent set in a graph is a set of vertices without edges between them. Every planar graph has an independent set of size at least 1/4n, and there are planar graphs for which no larger independent sets are possible.

In this paper, similar bounds are provided for the problem of bounded-degree independent set, i.e. an independent set where additionally all vertices have degree less than a pre-specified bound D. Our upper and lower bounds match (up to a small constant) for D ≤ 16.

Research partially supported by NSERC.

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References

  1. K. Appel and W. Haken. Every planar map is four colorable. I. Discharging. Illinois Journal of Mathematics, 21(3):429–490, 1977.

    MATH  MathSciNet  Google Scholar 

  2. M. Albertson. A lower bound for the independence number of a planar graph. Journal of Combinatorial Theory (B), 20:84–93, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Baker. Approximation algorithms for NP-complete problems on planar graphs. Journal of the ACM, 41(1):153–180, January 1994.

    Google Scholar 

  4. T. Biedl. Large independent sets in planar graphs in linear time. Technical report, Department of Computer Science, University of Waterloo, 1999.

    Google Scholar 

  5. H. Edelsbrunner. Algorithms in combinatorial geometry. Springer-Verlag, Berlin, 1987.

    MATH  Google Scholar 

  6. J. Iacono. Optimal planar point location. In Twelfth Annual ACM-SIAM Symposium On Discrete Algorithms, pages 340–341, New York, 2001. ACM.

    Google Scholar 

  7. D. Kirkpatrick. Optimal search in planar subdivisions. SIAM Journal of Computing, 12(1):28–35, February 1983.

    Google Scholar 

  8. R. Lipton and R. E. Tarjan. Applications of a planar separator theorem. SIAM Journal of Computing, 9(3):615–627, August 1980.

    Google Scholar 

  9. N. Robertson, D. Sanders, P. Seymour, and R. Thomas. The four-colour theorem. JCTB: Journal of Combinatorial Theory, Series B, 70:2–44, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Snoeyink and M. van Kreveld. Linear-time reconstruction of Delau-nay triangulations with applications. In Algorithms: 5th Annual European Symposium (ESA’ 97), pages 459–471, Berlin, 1997. Springer-Verlag.

    Google Scholar 

  11. D. F. Wilkinson. Bounded-degree independent sets. Master’s thesis, School of Computer Science, University of Waterloo, May 2002.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    Therese Biedl & Dana F. Wilkinson

Authors
  1. Therese Biedl
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  2. Dana F. Wilkinson
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Biedl, T., Wilkinson, D.F. (2002). Bounded-Degree Independent Sets in Planar Graphs. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_37

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  • DOI: https://doi.org/10.1007/3-540-36136-7_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00142-3

  • Online ISBN: 978-3-540-36136-7

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