On the number of edges in a uniform hypergraph with a range of permitted intersections |
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| Authors: | A?V?Bobu A?E?Kupriyanov Email author" target="_blank">A?M?RaigorodskiiEmail author |
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| Institution: | 1.Mechanics and Mathematics Faculty,Moscow State University,Moscow,Russia;2.Moscow Institute of Physics and Technology (State University),Dolgoprudnyi, Moscow oblast,Russia;3.Institute of Mathematics and Computer Science,Buryat State University,Ulan-Ude, Buryat Republic,Russia |
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| Abstract: | The paper studies the quantity p(n, k, t 1, t 2) equal to the maximum number of edges in a k-uniform hypergraph with the property that the size of the intersection of any two edges lies in the interval t 1, t 2]. Previously known upper and lower bounds are given. New bounds for p(n, k, t 1, t 2) are obtained, and the relationship between these bounds and known estimates is studied. For some parameter values, the exact values of p(n, k, t 1, t 2) are explicitly calculated. |
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