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Planar Graph Problems

  • Chapter
Computational Graph Theory

Part of the book series: Computing Supplementum ((COMPUTING,volume 7))

Abstract

Planar Graph Problems. Classical and recent results are surveyed in the development of efficient algorithms for the following eleven famous problems on planar graphs: planarity testing, embedding, drawing, separators, vertex-coloring, independent vertex set, listing subgraphs, Hamiltonian cycle, network flows, and Steiner trees and forests. Also typical methods and techniques useful for computational problems on planar graphs are discussed. Furthermore open questions on planar graphs are mentioned.

AMS Subject Classification: 05.

Zusammenfassung

Probleme anf plaoaren Graphen. In dieser Arbeit wird über klassische und jüngste Ergebnisse bei der Entwicklung efficienter Algorithmen für die folgenden elf wohlbekannten Probleme an planaren Graphen berichtet: Planaritätstests, Einbettung und Zeichnen, Separation, Knotenfärbung, Kantenfärbung, Unabhängige Knotenmengen, Auflisten von Untergraphen, Hamiltonsche Kreise, Netzwerkflüsse, Steiner Bäume und Wälder. Ferner werden typische Methoden und Techniken zur Behandlung planarer Graphen diskutiert. Einige olTene Fragen bezüglich planarer Graphen werden erwähnt.

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Authors and Affiliations

  1. Department of Electrical Communications Faculty of Engineering, Tohoku University, Sendai 980, Japan

    Takao Nishizeki

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  1. Takao Nishizeki
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Editors and Affiliations

  1. Institut für Mathematik, Technische Universität München, Federal Republic of Germany

    G. Tinhofer

  2. Department of Computer Science, Stanford University, Calif., USA

    E. Mayr

  3. Institut für Informatik, Universität Würzburg, Federal Republic of Germany

    H. Noltemeier

  4. Institute of Computer Science, University of Wrocław, Poland

    M. M. Syslo

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Nishizeki, T. (1990). Planar Graph Problems. In: Tinhofer, G., Mayr, E., Noltemeier, H., Syslo, M.M. (eds) Computational Graph Theory. Computing Supplementum, vol 7. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9076-0_3

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  • DOI: https://doi.org/10.1007/978-3-7091-9076-0_3

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