Victor Falgas-ravry

activity

20112026

most citedGlobal Structural Properties of Random Graphs

18 citations · 48 across the 33 of their papers we have counts for

collaborators

40 papers

math.CO2026

The threshold for the asymmetric vertex-Ramsey property in randomly perturbed graphs

Asier Calbet, Victor Falgas-Ravry, Joseph Hyde

For $r \geq 2$ and graphs $H_{1}, \dots, H_{r}, G$ , we say that $G$ is $(H_{1}, \dots, H_{r})$ vertex-Ramsey, or $(H_{1}, \dots, H_{r})_{v}$ -Ramsey, if whenever we colour the vertices of $G$ …

math.CO2026

Induced poset saturation in the hypergrid

R. Altar Ciceksiz, Victor Falgas-Ravry, Sabrina Lato +1

Set $[n] = {1, 2, \dots, n}$ . The hypergrid $[t]^{n}$ is the collection of functions $f : [n] \to [t]$ . We equip it with the natural partial order by letting $f \leq g$ when…

math.CO2025

On problems in extremal multigraph theory

Victor Falgas-Ravry, Adva Mond, Rik Sarkar +1

A multigraph G is said to be an (s,q)-graph if every s-set of vertices in G supports at most q edges (counting multiplicities). In this paper we consider the maximal sum and produc…

math.PR2025

Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups

Jason Behrstock, R. Altar Ciceksiz, Victor Falgas-Ravry

We consider random right-angled Coxeter groups, $W_{Γ}$ , whose presentation graph $Γ$ is taken to be an Erdős--Rényi random graph, i.e., $Γ \sim G_{n, p}$ . We use techniques…

math.GR2024★ 1 cited

A threshold for relative hyperbolicity in random right-angled Coxeter groups

Jason Behrstock, Recep Altar Ciceksiz, Victor Falgas-Ravry

We consider the random right-angled Coxeter group $W_{Γ}$ whose presentation graph $Γ \sim G_{n, p}$ is an Erd{\H o}s--Rényi random graph on $n$ vertices with edge probabilit…

math.CO2024

A note on locating-dominating sets in twin-free graphs

Nicolas Bousquet, Quentin Chuet, Victor Falgas-Ravry +2

In this short note, we prove that every twin-free graph on $n$ vertices contains a locating-dominating set of size at most $⌈ \frac{5}{8} n ⌉$ . This improves the earlier bou…

math.CO2023

Dedekind's problem in the hypergrid

Victor Falgas-Ravry, Eero Räty, István Tomon

Consider the partially ordered set on $[t]^{n} := {0, \dots, t - 1}^{n}$ equipped with the natural coordinate-wise ordering. Let $A (t, n)$ denote the number of antichains of this poset. The…

math.CO2023

Minimum degree conditions for rainbow triangles

Victor Falgas-Ravry, Klas Markström, Eero Räty

Let $G := (G_{1}, G_{2}, G_{3})$ be a triple of graphs on a common vertex set $V$ of size $n$ . A rainbow triangle in $G$ is a triple of edges $(e_{1}, e_{2}, e_{3})$ with $e_i\…

math.CO2023★ 1 cited

On density conditions for transversal trees in multipartite graphs

Leila Badakhshian, Victor Falgas-Ravry, Maryam Sharifzadeh

Let $G$ be an $r$ -partite graph such that the edge density between any two parts is at least $α$ . How large does $α$ need to be to guarantee that $G$ contains a connected transvers…

math.CO2022

Rainbow variations on a theme by Mantel: extremal problems for Gallai colouring templates

Victor Falgas-Ravry, Klas Markström, Eero Räty

Let $G := (G_{1}, G_{2}, G_{3})$ be a triple of graphs on the same vertex set $V$ of size $n$ . A rainbow triangle in $G$ is a triple of edges $(e_{1}, e_{2}, e_{3})$ with $e_i\…

math.CO2021

The codegree threshold of $K_{4}^{-}$

Victor Falgas-Ravry, Oleg Pikhurko, Emil R. Vaughan +1

The codegree threshold $ex_{2} (n, F)$ of a $3$ -graph $F$ is the minimum $d = d (n)$ such that every $3$ -graph on $n$ vertices in which every pair of vertices is contained in at…

math.PR2021

Bootstrap percolation in random geometric graphs

Victor Falgas-Ravry, Amites Sarkar

Following Bradonjić and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the $2$ -dimensional torus. In this model, the expected number of…

math.CO2021

Rectilinear approximation and volume estimates for hereditary bodies via [0,1]-decorated containers

Victor Falgas-Ravry, Robert Hancock, Johanna Strömberg +1

We use the hypergraph container theory of Balogh--Morris--Samotij and Saxton--Thomason to obtain general rectilinear approximations and volume estimates for sequences of bodies clo…

math.CO2021

$1$ -independent percolation on $Z^{2} \times K_{n}$

Victor Falgas-Ravry, Vincent Pfenninger

A random graph model on a host graph H is said to be 1-independent if for every pair of vertex-disjoint subsets A,B of E(H), the state of edges (absent or present) in A is independ…

math.CO2021

On an extremal problem for locally sparse multigraphs

Victor Falgas-Ravry

A multigraph $G$ is an $(s, q)$ -graph if every $s$ -set of vertices in $G$ supports at most $q$ edges of $G$ , counting multiplicities. Mubayi and Terry posed the problem of determini…

math.CO2020

Extremal problems for multigraphs

A. Nicholas Day, Victor Falgas-Ravry, Andrew Treglown

An $(n, s, q)$ -graph is an $n$ -vertex multigraph in which every $s$ -set of vertices spans at most $q$ edges. Turán-type questions on the maximum of the sum of the edge multiplicities…

math.PR2020

Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups

Jason Behrstock, Victor Falgas-Ravry, Tim Susse

Given a graph $Γ$ , its auxiliary \emph{square-graph} $□ (Γ)$ is the graph whose vertices are the non-edges of $Γ$ and whose edges are the pairs of non-edges which induce a squ…

math.CO2019

Existence thresholds and Ramsey properties of random posets

Victor Falgas-Ravry, Klas Markström, Andrew Treglown +1

Let $P (n)$ denote the power set of $[n]$ , ordered by inclusion, and let $P (n, p)$ denote the random poset obtained from $P (n)$ by retaining each element…

math.PR2019

Long paths and connectivity in { $1$ }-independent random graphs

A. Nicholas Day, Victor Falgas-Ravry, Robert Hancock

Given a graph $G$ , a probability measure $μ$ on the subsets of the edge set of $G$ is said to be $1$ -independent if events determined by edge sets that are at graph distance at lea…

math.CO2019

Maker-Breaker Percolation Games II: Escaping to Infinity

A. Nicholas Day, Victor Falgas-Ravry

Let $Λ$ be an infinite connected graph, and let $v_{0}$ be a vertex of $Λ$ . We consider the following positional game. Two players, Maker and Breaker, play in alternating turns. Init…

math.CO2019

Triangle-degrees in graphs and tetrahedron coverings in 3-graphs

Victor Falgas--Ravry, Klas Markström, Yi Zhao

We investigate a covering problem in $3$ -uniform hypergraphs ( $3$ -graphs): given a $3$ -graph $F$ , what is $c_{1} (n, F)$ , the least integer $d$ such that if $G$ is an $n$ -vertex $3$ -gr…

math.CO2018

Maker-Breaker Percolation Games I: Crossing Grids

A. Nicholas Day, Victor Falgas-Ravry

Motivated by problems in percolation theory, we study the following 2-player positional game. Let $Λ_{m \times n}$ be a rectangular grid-graph with $m$ vertices in each row and $n$ …

math.CO2018★ 1 cited

Multicolour containers, extremal entropy and counting

Victor Falgas-Ravry, Kelly O'Connell, Andrew Uzzell

In breakthrough results, Saxton-Thomason and Balogh-Morris-Samotij developed powerful theories of hypergraph containers. In this paper, we explore some consequences of these theori…

math.CO2016

Subgraphs with large minimum $ℓ$ -degree in hypergraphs where almost all $ℓ$ -degrees are large

Victor Falgas-Ravry, Allan Lo

Let $G$ be an $r$ -uniform hypergraph on $n$ vertices such that all but at most $ε (ℓ n)$ $ℓ$ -subsets of vertices have degree at least $p \binom{n-\ell}{r-\el…

The threshold for the asymmetric vertex-Ramsey property in randomly perturbed graphs

Induced poset saturation in the hypergrid

On problems in extremal multigraph theory

Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups

A threshold for relative hyperbolicity in random right-angled Coxeter groups

A note on locating-dominating sets in twin-free graphs

Dedekind's problem in the hypergrid

Minimum degree conditions for rainbow triangles

On density conditions for transversal trees in multipartite graphs

Rainbow variations on a theme by Mantel: extremal problems for Gallai colouring templates

The codegree threshold of K4−​

Bootstrap percolation in random geometric graphs

Rectilinear approximation and volume estimates for hereditary bodies via [0,1]-decorated containers

1-independent percolation on Z2×Kn​

On an extremal problem for locally sparse multigraphs

Extremal problems for multigraphs

Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups

Existence thresholds and Ramsey properties of random posets

Long paths and connectivity in {1}-independent random graphs

Maker-Breaker Percolation Games II: Escaping to Infinity

Triangle-degrees in graphs and tetrahedron coverings in 3-graphs

Maker-Breaker Percolation Games I: Crossing Grids

Multicolour containers, extremal entropy and counting

Subgraphs with large minimum ℓ-degree in hypergraphs where almost all ℓ-degrees are large

The codegree threshold of $K_{4}^{-}$

$1$ -independent percolation on $Z^{2} \times K_{n}$

Long paths and connectivity in { $1$ }-independent random graphs

Subgraphs with large minimum $ℓ$ -degree in hypergraphs where almost all $ℓ$ -degrees are large