Sylwia Antoniuk

activity

20132025

most citedFreiheitssatz and phase transition for the density model of random groups

14 citations · 36 across the 10 of their papers we have counts for

collaborators

11 papers

math.CO2025

Powers of Hamiltonian cycles in randomly augmented Pósa-Seymour graphs

Sylwia Antoniuk, Andrzej Dudek, Andrzej Ruciński

We study the question of the least number of random edges that need to be added to a Pósa-Seymour graph, that is, a graph with minimum degree exceeding $\frac{k}{k + 1} n$ , to secure t…

math.CO2024

Clique factors in randomly perturbed graphs: the transition points

Sylwia Antoniuk, Nina Kamčev, Christian Reiher

A randomly perturbed graph $G^{p} = G_{α} \cup G (n, p)$ is obtained by taking a deterministic $n$ -vertex graph $G_{α} = (V, E)$ with minimum degree $δ (G) \geq α n$ and adding the edges of the…

math.CO2024

Sets and partitions minimising small differences

Sylwia Antoniuk, Christian Reiher

For a bounded measurable set $A \subseteq R$ we denote the Lebesgue measure of ${(x, y) \in A^{2} : x \leq y \leq x + 1}$ by $Φ (A)$ . We prove that if $I=A_1\cup\dots\cup A_{k+…

math.CO2022

Powers of Hamiltonian cycles in randomly augmented Dirac graphs -- the complete collection

Sylwia Antoniuk, Andrzej Dudek, Andrzej Ruciński

We study the powers of Hamiltonian cycles in randomly augmented Dirac graphs, that is, $n$ -vertex graphs $G$ with minimum degree at least $(1/2 + ε) n$ to which some random…

math.GR2021★ 14 cited

Freiheitssatz and phase transition for the density model of random groups

Tsung-Hsuan Tsai

Magnus' Freiheitssatz states that if a group is defined by a presentation with $m$ generators and a single relator containing the last generating letter, then the first $m - 1$ lette…

math.CO2020

Properly colored Hamilton cycles in Dirac-type hypergraphs

Sylwia Antoniuk, Nina Kamčev, Andrzej Ruciński

We consider a robust variant of Dirac-type problems in $k$ -uniform hypergraphs. For instance, we prove that if $H$ is a $k$ -uniform hypergraph with minimum codegree at least $(1/2…

math.CO2020

High powers of Hamiltonian cycles in randomly augmented graphs

Sylwia Antoniuk, Andrzej Dudek, Christian Reiher +2

We investigate the existence of powers of Hamiltonian cycles in graphs with large minimum degree to which some additional edges have been added in a random manner. For all integers…

math.CO2015★ 4 cited

On the connectivity Waiter-Client game

Sylwia Antoniuk, Codruut Grosu, Lothar Narins

In this short note we consider a variation of the connectivity Waiter-Client game $W C (n, q, A)$ played on an $n$ -vertex graph $G$ which consists of $q + 1$ disjoint spanning…

math.GR2014

A sharp threshold for collapse of the random triangular group

Sylwia Antoniuk, Ehud Friedgut, Tomasz Łuczak

The random triangular group $Γ (n, p)$ is the group given by a random group presentation with $n$ generators in which every relator of length three is present independently with prob…

math.GR2013★ 13 cited

Random triangular groups at density 1/3

Sylwia Antoniuk, Tomasz Łuczak, Jacek Świcatkowski

Let Γ(n,p) denote the binomial model of a random triangular group. We show that there exist constants c, C > 0 such that if p <= c/n^2, then a.a.s. Γ(n,p) is free and if p >= C log…

math.GR2013★ 5 cited

Collapse of random triangular groups: a closer look

Sylwia Antoniuk, Tomasz Łuczak, Jacek Świcatkowski

The random triangular group Γ(n,t) is a group given by a presentation P=<S|R>, where S is a set of n generators and R is a random set of t cyclically reduced words of length three.…