Asier Calbet

activity

20212026

collaborators

7 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.CO2025

The maximum number of triangles in $K_{1, s, t}$ -free graphs

Asier Calbet, Ritesh Goenka

We consider the following generalized Turán problem: For $2 \leq s \leq t$ , what is the maximum number of triangles in a $K_{1, s, t}$ -free graph on $n$ vertices? The previously best k…

math.CO2024

Twin-free $K_{r}$ -saturated Graphs and Maximally Independent Sets in $K_{3}$ -free Graphs

Asier Calbet

We say that two vertices are twins if they have the same neighbourhood and that a graph is $K_{r}$ -saturated if it does not contain $K_{r}$ but adding any new edge to it creates a $K_r…

math.CO2024

The asymptotic behaviour of $s a t (n, F)$

Asier Calbet, Andrea Freschi

For a family $F$ of graphs, $s a t (n, F)$ is the minimum number of edges in a graph $G$ on $n$ vertices which does not contain any of the graphs in $F$ b…

math.CO2023

A collection of open problems in celebration of Imre Leader's 60th birthday

Rahil Baber, Natalie Behague, Asier Calbet +10

One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems…

math.CO2023

$K_{r}$ -saturated Graphs and the Two Families Theorem

Asier Calbet

Given a graph $H$ , we say that a graph $G$ is $H$ -saturated if $G$ contains no copy of $H$ but adding any new edge to $G$ creates a copy of $H$ . Let $s a t (n, K_{r}, t)$ be the minimum n…

math.CO2021

The Number of Locally $p$ -stable Functions on $Q_{n}$

Asier Calbet

A Boolean function $f : V \to {- 1, 1}$ on the vertex set of a graph $G = (V, E)$ is locally $p$ -stable if for every vertex $v$ the proportion of neighbours $w$ of $v$ with $f (v) = f (w)$ …

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

The maximum number of triangles in K1,s,t​-free graphs

Twin-free Kr​-saturated Graphs and Maximally Independent Sets in K3​-free Graphs

The asymptotic behaviour of sat(n,F)

A collection of open problems in celebration of Imre Leader's 60th birthday

Kr​-saturated Graphs and the Two Families Theorem

The Number of Locally p-stable Functions on Qn​

The maximum number of triangles in $K_{1, s, t}$ -free graphs

Twin-free $K_{r}$ -saturated Graphs and Maximally Independent Sets in $K_{3}$ -free Graphs

The asymptotic behaviour of $s a t (n, F)$

$K_{r}$ -saturated Graphs and the Two Families Theorem

The Number of Locally $p$ -stable Functions on $Q_{n}$