Andrzej Ruci'nski

activity

20232026

collaborators

6 papers

math.CO2026

Homogeneous substructures in random ordered uniform matchings

Andrzej Dudek, Jarosław Grytczuk, Jakub Przybyło +1

An ordered $r$ -uniform matching of size $n$ is a collection of $n$ pairwise disjoint $r$ -subsets of a linearly ordered set of $r n$ vertices. For $n = 2$ , such a matching is called an…

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.CO2025

Homogeneous substructures in random ordered hyper-matchings

Andrzej Dudek, Jarosław Grytczuk, Jakub Przybyło +1

An ordered $r$ -uniform matching of size $n$ is a collection of $n$ pairwise disjoint $r$ -subsets of a linearly ordered set of $r n$ vertices. For $n = 2$ , such a matching is called an…

math.CO2025

Shuffle squares and ordered nest-free graphs

Jarosław Grytczuk, Bartłomiej Pawlik, Andrzej Ruciński

A shuffle square is a word consisting of two shuffled copies of the same word. For instance, the Turkish word $\mathtt{\color{red}{ik}\color{blue}{i}\color{red}{li}\color{blue}{kli…

math.CO2024

Largest bipartite sub-matchings of a random ordered matching or a problem with socks

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

Let $M$ be an ordered matching of size $n$ , that is, a partition of the set $[2 n]$ into 2-element subsets. The sock number of $M$ is the maximum size of a sub-matching of $M$ in wh…

math.CO2023

Twins in ordered hyper-matchings

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

An ordered $r$ -matching of size $n$ is an $r$ -uniform hypergraph on a linearly ordered set of vertices, consisting of $n$ pairwise disjoint edges. Two ordered $r$ -matchings are iso…