Coloring planar perfect graphs by decomposition


This paper describes a decomposition scheme for coloring perfect graphs. Based on this scheme, one need only concentrate on coloring highly connected (at least 3-connected) perfect graphs. This idea is illustrated on planar perfect graphs, which yields a straightforward coloring algorithm. We suspect that, under appropriate definition, highly connected perfect graphs might possess certain regular properties that are amenable to coloring algorithms.

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  1. [1]

    C. Berge,Graphs and Hypergraphs, North Holland, 1973, Amsterdam.

    MATH  Google Scholar 

  2. [2]

    M. Grötschel, L. Lovász andA. Schrijver, The ellipsoid method and its consequences in combinatorial optimization,Combinatorica 1 (1981), 169–197.

    MATH  MathSciNet  Google Scholar 

  3. [3]

    W.-L. Hsu, Decomposition of perfect graphs,to appear in J. Combin. Theory (B). (1987).

  4. [4]

    W.-L. Hsu, Recognizing planar perfect graphs,to appear in J. Assoc. Comput. Mach. (1987).

  5. [5]

    W.-L. Hus,A polynomial algorithm for the maximum independent set problem on planar perfect graphs, Technical Report, Northwestern University, Evanston, Illinois, (1984).

    Google Scholar 

  6. [6]

    A. Tucker, The strong perfect graph conjecture for planar graphs,Canadian Journal of Mathematics 25 (1973), 103–114.

    MATH  MathSciNet  Google Scholar 

  7. [7]

    A. Tucker, AnO(n 2) algorithm for coloring perfect planar graphs,Journal of Algorithms 5 (1984), 60–68.

    MATH  Article  MathSciNet  Google Scholar 

  8. [8]

    R. J. Wilson,Introduction to Graph Theory, Academic Press, New York, (1972).

    MATH  Google Scholar 

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This research has been supported in part by National Science Foundation under grant ECS—8105989 to Northwestern University.

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Hsu, W.L. Coloring planar perfect graphs by decomposition. Combinatorica 6, 381–385 (1986).

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AMS subject classification (1980)

  • 05 C 15