S. Antoniuk

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math.CO2025

Powers of Hamiltonian cycles in randomly augmented PÃ³sa-Seymour graphs

Sylwia Antoniuk, Andrzej Dudek, Andrzej RuciÅski

We study the question of the least number of random edges that need to be added to a PÃ³sa-Seymour graph, that is, a graph with minimum degree exceeding $\frac{k}{k + 1} n$ , to secure…

math.CO2024

Clique factors in randomly perturbed graphs: the transition points

Sylwia Antoniuk, Nina KamÄev, Christian Reiher

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

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 $I^¦ (A)$ . We prove that if $I=A_1\cup\dots\cup A_{k…