Extremal hypergraph problems and convex hulls

Abstract

Theprofile of a hypergraph onn vertices is (f 0, f1, ...,f n) wheref i denotes the number ofi-element edges. The extreme points of the set of profiles is determined for certain hypergraph classes. The results contain many old theorems of extremal set theory as particular cases (Sperner. Erdős—Ko—Rado, Daykin—Frankl—Green—Hilton).

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References

  1. [1]

    D. E. Daykin, P. Frankl, C. Greene, andA. J. W. Hilton, A generalization of Sperner’s theorem,J. of the Austral. Math. Soc. A,31 (1981), 481–485.

    MATH  MathSciNet  Article  Google Scholar 

  2. [2]

    K. Engel,submitted to Combinatorica.

  3. [3]

    P. Erdős, On a lemma of Littlewood and Offord,Bull. of the Amer. Math. Soc.,51 (1945), 898–902.

    Article  Google Scholar 

  4. [4]

    P. Erdős, Chao Ko, andR. Rado, Intersection theorems for systems of finite sets,Quart. J. Math. Oxford (2),12 (1961), 313–318.

    Article  Google Scholar 

  5. [5]

    Péter L. Erdős, P. Frankl, andG. O. H. Katona, Intersecting Sperner families and their convex hulls,Combinatorica,4 (1984), 21–34.

    Article  MathSciNet  Google Scholar 

  6. [6]

    G. O. H. Katona, Intersection theorems for system of finite sets,Acta Math. Acad. Sci. Hungar.,15 (1964), 329–337.

    MATH  Article  MathSciNet  Google Scholar 

  7. [7]

    G. O. H. Katona, A simple proof of the Erdős—Chao Ko—Rado theorem,J. Combinatorial Th. B,13 (1972), 183–184.

    MATH  Article  MathSciNet  Google Scholar 

  8. [8]

    E. Sperner, Ein Satz über Untermenge einer endlichen Menge,Mat. Z.,27 (1928), 544–548.

    Article  MathSciNet  MATH  Google Scholar 

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Erdős, P.L., Katona, G.O.H. & Frankl, P. Extremal hypergraph problems and convex hulls. Combinatorica 5, 11–26 (1985). https://doi.org/10.1007/BF02579438

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 65, 52 A 20