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
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References
Albertson, M. O., "A Lower Bound for the Independence Number of a Planar Graph", J. Combinatorial Theory, submitted.
Berge, C., Graphes et Hypergraphes, Dunod, Paris, 1970.
Haken, W., "An Existence Theorem for Planar Maps", J. Combinatorial Theory 14B, 1973.
Kotzig, A., "Contribution to the Theory of Eulerian Polyhedra", Mat. Fyz. Casopis 5 (1955) 101–113.
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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
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