A class of constructions for turán’s (3, 4)-problem |
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Authors: | A V Kostochka |
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Institution: | (1) Institute of Mathematics of the Siberian Branch of the Academy of Sciences of the USSR, 630090 Novosibirsk-90, USSR |
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Abstract: | Letf(n) denote the minimal number of edges of a 3-uniform hypergraphG=(V, E) onn vertices such that for every quadrupleY ⊂V there existsY ⊃e ∈E. Turán conjectured thatf(3k)=k(k−1)(2k−1). We prove that if Turán’s conjecture is correct then there exist at least 2
k−2 non-isomorphic extremal hypergraphs on 3k vertices. |
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Keywords: | 05 C 35 05 C 65 |
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