On a geometric property of perfect graphs


LetG be a graph,VP(G) its vertex packing polytope and letA(G) be obtained by reflectingVP(G) in all Cartersian coordinates. Denoting byA*(G) the set obtained similarly from the fractional vertex packing polytope, we prove that the segment connecting any two non-antipodal vertices ofA(G) is contained in the surface ofA(G) and thatG is perfect if and only ifA*(G) has a similar property.

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  1. [1]

    V. Chvátal, On certain polytopes assotiated with graphs,Centre de Recherche Mathematique, Univ. de Montreal, Que., CRM238, 1972.

  2. [2]

    D. R. Fulkerson, Antiblocking polyhedra,J. Combinatorial Theory (B) 12 (1972) 50–71.

    MATH  Article  MathSciNet  Google Scholar 

  3. [3]

    D. R. Fulkerson, Blocking and antiblocking pairs of polyhedra,Mathematical Programming 1 (1971) 168–194.

    MATH  Article  MathSciNet  Google Scholar 

  4. [4]

    L. Lovász, Normal hypergraphs and the perfect graph conjecture,Discrete Mathematics 2 (1972) 353–267.

    Article  Google Scholar 

  5. [5]

    L. Lovász, A characterization of perfect graphs,J. Combinatorial Theory (B) 13 (1972) 95–98.

    MATH  Article  Google Scholar 

  6. [6]

    M. Padberg, Almost integral polyhedra related to certain combinatorial optimization problems,Linear Algebra and its Applications, Vol.15 (1976) 63–88.

    Article  MathSciNet  Google Scholar 

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Zaremba, L.S., Perz, S. On a geometric property of perfect graphs. Combinatorica 2, 395–397 (1982). https://doi.org/10.1007/BF02579436

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AMS subject classification 1980

  • 05 C 99
  • 52 A 25