Neal Bushaw

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The Turán number of an r-uniform hypergraph H is the maximum number of edges in any r-graph on n vertices which does not contain H as a subgraph. Let P denote the family of r-uniform loose paths on edges, F(k, l) denote the family of hypergraphs consisting of k disjoint paths from P , and L (r) denote an r-uniform linear path on edges. We determine(More)
In 1987, Kolaitis, Prömel and Rothschild proved that, for every fixed r ∈ N, almost every n-vertex Kr+1-free graph is r-partite. In this paper we extend this result to all functions r = r(n) with r 6 (log n). The proof combines a new (close to sharp) supersaturation version of the Erdős–Simonovits stability theorem, the hypergraph container method, and a(More)
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