A. Dudek

activity

20242026

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5 papers · 1 filter

math.CO2026

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.CO2026

Homogeneous substructures in random ordered hyper-matchings

Andrzej Dudek, JarosÅaw Grytczuk, Jakub PrzybyÅo +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.CO2026

Homogeneous substructures in random ordered uniform matchings

Andrzej Dudek, JarosÅaw Grytczuk, Jakub PrzybyÅo +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 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

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

Andrzej Dudek, JarosÅaw Grytczuk, Andrzej RuciÅski

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…