The Number of Hypergraphs without Linear Cycles
نویسندگان
چکیده
The r-uniform linear k-cycle C k is the r-uniform hypergraph on k(r−1) vertices whose edges are sets of r consecutive vertices in a cyclic ordering of the vertex set chosen in such a way that every pair of consecutive edges share exactly one vertex. Here, we prove a balanced supersaturation result for linear cycles which we then use in conjunction with the method of hypergraph containers to show that for any fixed pair of integers r, k ≥ 3, the number of C k-free r-uniform hypergraphs on n vertices is 2 Θ(n), thereby settling a conjecture due to Mubayi and Wang from 2017.
منابع مشابه
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تاریخ انتشار 2017