New asymptotics for bipartite Tura´n numbers
Journal of Combinatorial Theory Series A
Norm-graphs: variations and applications
Journal of Combinatorial Theory Series B
Extremal problems for sets forming Boolean algebras and complete partite hypergraphs
Journal of Combinatorial Theory Series A
Extremal Graph Theory
New lower bounds for Ramsey numbers of graphs and hypergraphs
Advances in Applied Mathematics - Special issue: Memory of Rodica Simon
On the spectrum of projective norm-graphs
Information Processing Letters
A hypergraph extension of the bipartite Turán problem
Journal of Combinatorial Theory Series A
The maximum size of hypergraphs without generalized 4-cycles
Journal of Combinatorial Theory Series A
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Given a family ℱ of r-graphs, let ex(n, ℱ) be the maximum number of edges in an n-vertex r-graph containing no member of ℱ. Let C(r) 4 denote the family of r-graphs with distinct edges A, B, C, D, such that A ∩ B = C ∩ D = Ø and A ∪ B = C ∪ D. For s1 ⩽ … ⩽ sr, let K(r) (s1,…,sr) be the complete r-partite r-graph with parts of sizes s1,…,sr.Füredi conjectured over 15 years ago that ex(n,C(3)4) ⩽ (n2) for sufficiently large n. We prove the weaker resultex(n, {C(3)4, K(3)(1,2,4)}) ⩽ (n2).Generalizing a well-known conjecture for the Turán number of bipartite graphs, we conjecture thatex(n, K(r)(s1,…,sr)) = Θ(nr−1/s),where s = Πr−1i=1 si. We prove this conjecture when s1 = … = sr−2 = 1 and(i) sr−1 = 2, (ii) sr−1 = sr = 3, (iii)sr (sr−1−1)!.In cases (i) and (ii), we determine the asymptotic value of ex(n,K(r)(s1,…,sr)).We also provide an explicit construction givingex(n,K(3)(2,2,3)) (1/6−o(1))n8/3.This improves upon the previous best lower bound of &OHgr;(n29/11) obtained by probabilistic methods. Several related open problems are also presented.