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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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.
K. Engel,submitted to Combinatorica.
P. Erdős, On a lemma of Littlewood and Offord,Bull. of the Amer. Math. Soc.,51 (1945), 898–902.
P. Erdős, Chao Ko, andR. Rado, Intersection theorems for systems of finite sets,Quart. J. Math. Oxford (2),12 (1961), 313–318.
Péter L. Erdős, P. Frankl, andG. O. H. Katona, Intersecting Sperner families and their convex hulls,Combinatorica,4 (1984), 21–34.
G. O. H. Katona, Intersection theorems for system of finite sets,Acta Math. Acad. Sci. Hungar.,15 (1964), 329–337.
G. O. H. Katona, A simple proof of the Erdős—Chao Ko—Rado theorem,J. Combinatorial Th. B,13 (1972), 183–184.
E. Sperner, Ein Satz über Untermenge einer endlichen Menge,Mat. Z.,27 (1928), 544–548.
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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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DOI: https://doi.org/10.1007/BF02579438