Emil Powierski

activity

20192026

most citedRamsey properties of randomly perturbed dense graphs

12 citations · 22 across the 9 of their papers we have counts for

collaborators

Showing math.COShow all

9 papers · 1 filter

math.CO2025

A local limit theorem for the edge counts of random induced subgraphs of a random graph

Paul Balister, Emil Powierski, Alex Scott +1

Consider a `dense' Erdős--Rényi random graph model $G = G_{n, M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M / (2 n)$ is bounded away from 0 and 1. Fix…

math.CO2023

A note on interval colourings of graphs

Maria Axenovich, António Girão, Lawrence Hollom +5

A graph is said to be interval colourable if it admits a proper edge-colouring using palette $N$ in which the set of colours incident to each vertex is an interval. The in…

math.CO2023

Reconstructing a point set from a random subset of its pairwise distances

António Girão, Freddie Illingworth, Lukas Michel +2

Let $V$ be a set of $n$ points on the real line. Suppose that each pairwise distance is known independently with probability $p$ . How much of $V$ can be reconstructed up to isometr…

math.CO2022★ 6 cited

Invertibility of digraphs and tournaments

Noga Alon, Emil Powierski, Michael Savery +2

For an oriented graph $D$ and a set $X \subseteq V (D)$ , the inversion of $X$ in $D$ is the digraph obtained by reversing the orientations of the edges of $D$ with both endpoints in…

math.CO2022★ 1 cited

Balancing connected colourings of graphs

Freddie Illingworth, Emil Powierski, Alex Scott +1

We show that the edges of any graph $G$ containing two edge-disjoint spanning trees can be blue/red coloured so that the blue and red graphs are connected and the blue and red degr…

math.CO2022★ 1 cited

Induced subgraphs of induced subgraphs of large chromatic number

António Girão, Freddie Illingworth, Emil Powierski +4

We prove that, for every graph $F$ with at least one edge, there is a constant $c_{F}$ such that there are graphs of arbitrarily large chromatic number and the same clique number as…

math.CO2021★ 2 cited

Counting partitions of $G_{n, 1/2}$ with degree congruence conditions

Paul Balister, Emil Powierski, Alex Scott +1

For $G = G_{n, 1/2}$ , the Erdős--Renyi random graph, let $X_{n}$ be the random variable representing the number of distinct partitions of $V (G)$ into sets $A_{1}, \dots, A_{q}$ so that th…

math.CO2021

A note on infinite antichain density

Paul Balister, Emil Powierski, Alex Scott +1

Let $F$ be an antichain of finite subsets of $N$ . How quickly can the quantities $∣ F \cap 2^{[n]} ∣$ grow as $n \to \infty$ ? We show that for any sequence…

math.CO2019★ 12 cited

Ramsey properties of randomly perturbed dense graphs

Emil Powierski

We investigate Ramsey properties of a random graph model in which random edges are added to a given dense graph. Specifically, we determine lower and upper bounds on the function $…

A local limit theorem for the edge counts of random induced subgraphs of a random graph

A note on interval colourings of graphs

Reconstructing a point set from a random subset of its pairwise distances

Invertibility of digraphs and tournaments

Balancing connected colourings of graphs

Induced subgraphs of induced subgraphs of large chromatic number

Counting partitions of Gn,1/2​ with degree congruence conditions

A note on infinite antichain density

Ramsey properties of randomly perturbed dense graphs

Counting partitions of $G_{n, 1/2}$ with degree congruence conditions