Distributed Computing

, Volume 7, Issue 1, pp 55–59 | Cite as

A self-stabilizing algorithm for coloring planar graphs

  • Sukumar Ghosh
  • Mehmet Hakan Karaata
Special Issue on Self-stabilization


This paper describes an algorithm for coloring the nodes of a planar graph with no more than six colors using a self-stabilizing approach. The first part illustrates the coloring algorithm on a directed acyclic version of the given planar graph. The second part describes a selfstabilizing algorithm for generating the directed acyclic version of the planar graph, and combines the two algorithms into one.

Key words

Self-stabilization Distributed algorithm-Graph coloring Directed acyclic graph Atomicity 


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  1. 1.
    Appel K, Haken W. Every planar map is four-colorable. Am Math Soc 98 (1989).Google Scholar
  2. 2.
    Chiba N, Nishizeki T, Saito N: A linear algorithm for fivecoloring of a planar graph. Proc 17th Symp of Research Institute of Electrical Communication (1980)Google Scholar
  3. 3.
    Dijkstra EW: Self-stabilizing system in spite of distributed control. Commun ACM 17(11):643–644 (1974)Google Scholar
  4. 4.
    Dijkstra EW: A belated proof of self-stabilization. Distrib Comput 1(1):5–6 (1986)Google Scholar
  5. 5.
    Harary F: Graph theory. Addison-Wesley, Reading, Mass., 1969Google Scholar
  6. 6.
    He Xin: Eficient parallel and sequential algorithms for 4-coloring perfect planar graphs. Algorithmica 5:545–559 (1990)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Sukumar Ghosh
    • 1
  • Mehmet Hakan Karaata
    • 1
  1. 1.Department of Computer ScienceUniversity of IowaIowa CityUSA

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