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Finding an independent set in a planar graph

Part III: Contributed Papers New Results On Graphs And Combinatorics

Part of the Lecture Notes in Mathematics book series (LNM,volume 406)

Abstract

A subset H of the vertices of a graph is independent if no two vertices in H are adjacent. The Erdös-Vizing Problem suggests that a planar graph has an independent set of vertices that contains at least 1/4 of the vertices of the graph. The purpose of this paper is to give an algorithm that produces an independent set in a planar graph that contains more than 2/9 of the vertices of the graph.

Keywords

  • Planar Graph
  • Existence Theorem
  • Combinatorial Theory
  • Separate Case
  • Interior Vertex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Albertson, M. O., "A Lower Bound for the Independence Number of a Planar Graph", J. Combinatorial Theory, submitted.

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  2. Berge, C., Graphes et Hypergraphes, Dunod, Paris, 1970.

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  3. Haken, W., "An Existence Theorem for Planar Maps", J. Combinatorial Theory 14B, 1973.

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  4. Kotzig, A., "Contribution to the Theory of Eulerian Polyhedra", Mat. Fyz. Casopis 5 (1955) 101–113.

    MathSciNet  Google Scholar 

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© 1974 Springer-Verlag Berlin

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Albertson, M.O. (1974). Finding an independent set in a planar graph. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066439

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  • DOI: https://doi.org/10.1007/BFb0066439

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

  • eBook Packages: Springer Book Archive