Sylwia Antoniuk

activity

20202025

collaborators

5 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.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…