Extremal Finite Set Theory surveys old and new results in the area of extremal set system
theory. It presents an overview of the main techniques and tools (shifting, the cycle method …

Fix graphs F and H and let ex (n, H, F) denote the maximum possible number of copies of
the graph H in an n-vertex F-free graph. The systematic study of this function was initiated by …

Let E(G) and V(G) denote the edge set and vertex set of a (hyper) graph G. Let G be a graph
and H be a hypergraph. We say that a hypergraph H is a Berge-G if there is a bijection …

For a graph F, a hypergraph H is a Berge copy of F (or a Berge-F in short), if there is a
bijection f: E (F)→ E (H) such that for each e∈ E (F) we have e⊂ f (e). A hypergraph is Berge …

Let F be a graph. A hypergraph is called Berge-F if it can be obtained by replacing each
edge in F by a hyperedge containing it. Let F be a family of graphs. The Turán number of the …

Let n≥ k≥ r+ 3 and H be an n-vertex r-uniform hypergraph. We show that if| H|> n− 1 k− 2
(k− 1 r) then H contains a Berge cycle of length at least k. This bound is tight when k− 2 …

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Let F be a graph. We say that a hypergraph H is a Berge-F if there is a bijection f: E (F)→ E
(H) such that e⊆ f (e) for every e∈ E (F). Note that Berge-F actually denotes a class of …

The anti-Ramsey problem was introduced by Erdös, Simonovits, and Sós in 1970s. The
anti-Ramsey number of a hypergraph H, ar (n, s, H), is the smallest integer c such that in any …

We show that for each k≥ 4 and n> r≥ k+ 1, every n-vertex hypergraph with edge sizes at
least r and no Berge cycle of length at least k has at most (k− 1)(n− 1) r edges. The bound is …