A. Dudek

activity

20182026

collaborators

Showing math.COShow all

5 papers · 1 filter

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

Loose paths in random ordered hypergraphs

Andrzej Dudek, Alan Frieze, Wesley Pegden

We consider the length of {\em ordered loose paths} in the random $r$ -uniform hypergraph $H = H^{(r)} (n, p)$ . A ordered loose path is a sequence of edges $E_{1}, E_{2}, \dots, E_{ℓ}$ wher…

math.CO2018

Powers of Hamiltonian cycles in randomly augmented graphs

Andrzej Dudek, Christian Reiher, Andrzej Ruciński +1

We study 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. It follows from the th…