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- Victor Falgas-Ravry, Emil R. Vaughan
- Combinatorics, Probability & Computing
- 2013

- Victor Falgas-Ravry, Emil R. Vaughan
- Electr. J. Comb.
- 2012

- Victor Falgas-Ravry
- Electr. J. Comb.
- 2011

Let Ω be a finite set and let S ⊆ P(Ω) be a set system on Ω. For x ∈ Ω, we denote by d S (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 d S (x) ≥ 1 2 |S|. We consider a related question. Define the weight of a family S to be w(S) := A∈S |A|. Suppose S is… (More)

- Victor Falgas-Ravry, Edward Marchant, Oleg Pikhurko, Emil R. Vaughan
- SIAM J. Discrete Math.
- 2015

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 F 3,2 be the 3-graph on {a, b, c, d, e} with 3-edges abc, abd, abe and cde. In this… (More)

- Victor Falgas-Ravry
- Combinatorics, Probability & Computing
- 2015

- Victor Falgas-Ravry
- Electr. J. Comb.
- 2013

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)

- Victor Falgas-Ravry, Joel Larsson, Klas Markström
- ArXiv
- 2016

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 X 1 , X 2 ,. . ., where the X i are independent random variables with distribution given by X. The covering time T is the smallest integer t ≥ 0 such that t i=1 X i = V. The distribution of T is important in many… (More)

- Victor Falgas-Ravry, Kelly O’Connell, Johanna Strömberg, Andrew Uzzell
- 2016

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)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract Let S n,k denote the random geometric graph obtained by placing points inside a square of area n according to a Poisson point process of intensity 1 and joining each such point to the k = k(n) points of the process nearest to it. In this paper we show that if P(S n,k connected) > n −γ 1 then the… (More)

- Victor Falgas-Ravry, Klas Markström, Jacques Verstraëte
- ArXiv
- 2015

Let G = (V, E) be a graph of density p on n vertices. Following Erd˝ os, Luczak and Spencer [11], 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