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Line perfect graphs

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Abstract

The concept of line perfection of a graph is defined so that a simple graph is line perfect if and only if its line graph is perfect in the usual sense. Line perfect graphs are characterized as those which contain no odd cycles of size larger than 3. Two well-know theorems of König for bipartite graphs are shown to hold also for line perfect graphs; this extension provides a reinterpretation of the content of these theorems.

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References

  1. M.L. Balinski, “Establishing the matching polytope”,Journal of Combinatorial Theory 13 (1972) 1–13.

    Google Scholar 

  2. C. Berge, “Färbung von graphen, deren sämtliche bzw. deren ungerade kreise starr sind”,Wissenschaftliche Zeitschrift der Martin-Luther Universität Halle-Wittenberg Mathematisch-Naturwissenschaftliche Reihe (1961) 114.

  3. C. Berge, “Some classes of perfect graphs”, in: F. Harary, ed.,Graph theory and theoretical physics (Academic Press, New York, 1967).

    Google Scholar 

  4. C. Berge,Graphs and hypergraphs (North-Holland, New York, 1973).

    Google Scholar 

  5. V. Chvátal, “On certain polytopes associated with graphs”,Journal of Combinatorial Theory B18 (1975) 138–154.

    Google Scholar 

  6. J. Edmonds, “Paths, trees, and flowers”,Canadian Journal of Mathematics 17 (1965) 449–467.

    Google Scholar 

  7. J. Edmonds, “Maximum matching and a polyhedron with (0, 1)-vertices”,Journal of Research of the National Bureau of Standards 69B (1965) 125–130.

    Google Scholar 

  8. D.R. Fulkerson, “Blocking and anti-blocking pairs of polyhedra”,Mathematical Programming 1 (1971) 168–194.

    Google Scholar 

  9. D.R. Fulkerson, “Anti-blocking polyhedra”,Journal of Combinatorial Theory 12 (1972) 50–71.

    Google Scholar 

  10. D.R. Fulkerson, “On the perfect graph theorem”, in: T.C. Hu and S.M. Robinson, eds.,Mathematical programming (Academic Press, New York, 1973) pp. 69–76.

    Google Scholar 

  11. F. Harary,Graph theory (addison-Wesley, Reading, MA, 1969).

    Google Scholar 

  12. D. König,Theorie der endlichen und unendlichen graphen (Chelsea, New York, 1950).

    Google Scholar 

  13. L. Lovász, “A characterization of perfect graphs”,Journal of Combinatorial Theory B13 (1972) 95–98.

    Google Scholar 

  14. L. Lovász, “Normal hypergraphs and the perfect graph conjecture”,Discrete Mathematics 2 (1972) 253–267.

    Google Scholar 

  15. K.R. Parthasarathy and G. Ravindra, “The strong perfect-graph conjecture is true forK 1–3-free graphs”,Journal of Combinatorial Theory, to appear.

  16. W. Pulleyblank, “Faces of matching polyhedra”, Doctoral Dissertation, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario (1973).

    Google Scholar 

  17. L.E. Trotter, Jr., “Solution characteristics and algorithms for the vertex packing problem”, Tech. Rept. No. 168, Department of Operations Research, Cornell University, Ithaca, NY (1973).

    Google Scholar 

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Authors and Affiliations

  1. Cornell University, Ithaca, NY, USA

    L. E. Trotter Jr.

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  1. L. E. Trotter Jr.
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Supported by National Science Foundation Grants GK-42095 and ENG 76-09936.

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Trotter, L.E. Line perfect graphs. Mathematical Programming 12, 255–259 (1977). https://doi.org/10.1007/BF01593791

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  • DOI: https://doi.org/10.1007/BF01593791

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