Victor Falgas-Ravry

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Given an r-graph H on h vertices, and a family F of forbidden subgraphs, we define exH(n,F) to be the maximum number of induced copies of H in an F-free r-graph on n vertices. Then the Turán H-density of F is the limit πH(F) = lim n→∞ exH(n,F)/ ( n h ) . This generalises the notions of Turán density (when H is an r-edge), and inducibility (when F is empty).(More)
Let Ω be a finite set and let S ⊆ P(Ω) be a set system on Ω. For x ∈ Ω, we denote by dS(x) the number of members of S containing x. A long-standing conjecture of Frankl states that if S is union-closed then there is some x ∈ Ω with dS(x) ≥ 12 |S|. We consider a related question. Define the weight of a family S to be w(S) := ∑ A∈S |A|. Suppose S is(More)
Given a family of 3-graphs F , we define its codegree threshold coex(n,F) to be the largest number d = d(n) such that there exists an n-vertex 3-graph in which every pair of vertices is contained in at least d 3-edges but which contains no member of F as a subgraph. Let F3,2 be the 3-graph on {a, b, c, d, e} with 3-edges abc, abd, abe and cde. In this(More)
Given a 3-graph F , its codegree threshold co-ex(n, F ) is the largest number d = d(n) such that there exists an n-vertex 3-graph in which every pair of vertices is contained in at least d triples but which contains no member of F as a subgraph. The limit γ(F ) = lim n→∞ co-ex(n, F ) n− 2 is known to exist and is called the codegree density of F . In this(More)
Let V be an n-set, and let X be a random variable taking values in the powerset of V . Suppose we are given a sequence of random coupons X1, X2, . . ., where the Xi are independent random variables with distribution given by X . The covering time T is the smallest integer t ≥ 0 such that ⋃t i=1 Xi = V . The distribution of T is important in many(More)
In recent breakthrough results, Saxton–Thomason and Balogh–Morris–Samotij have developed powerful theories of hypergraph containers. These theories have led to a large number of new results on transference, and on counting and characterising typical graphs in hereditary properties. In a different direction, Hatami–Janson–Szegedy proved results on the(More)
Let G be a graph of density p on n vertices. Following Erdős, Luczak and Spencer [10], an m-vertex subgraph H of G is called full if H has minimum degree at least p(m− 1). Let f(G) denote the order of a largest full subgraph of G. If p ( n 2 ) is a positive integer, define fp(n) = min{f(G) : v(G) = n, e(G) = p ( n 2 ) }. Erdős, Luczak and Spencer [10](More)