A. Dudek

activity

20092023

most citedAn alternative proof of the linearity of the size-Ramsey number of paths

44 citations · 113 across the 33 of their papers we have counts for

collaborators

54 papers

math.CO2023★ 2 cited

Erdős-Szekeres type Theorems for ordered uniform matchings

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

For $r, n \geq 2$ , an ordered $r$ -uniform matching of size $n$ is an $r$ -uniform hypergraph on a linearly ordered vertex set $V$ , with $∣ V ∣ = r n$ , consisting of $n$ pairwise disjoint edg…

math.CO2022

A random coloring process gives improved bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers

Patrick Bennett, Andrzej Dudek, Sean English

The Erdős-Gyárfás number $f (n, p, q)$ is the smallest number of colors needed to color the edges of the complete graph $K_{n}$ so that all of its $p$ -clique spans at least $q$ colors…

math.CO2022★ 1 cited

Ordered unavoidable sub-structures in matchings and random matchings

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

An ordered matching of size $n$ is a graph on a linearly ordered vertex set $V$ , $∣ V ∣ = 2 n$ , consisting of $n$ pairwise disjoint edges. There are three different ordered matchings of…

math.CO2022

A note on non-isomorphic edge-color classes in random graphs

Patrick Bennett, Ryan Cushman, Andrzej Dudek +1

For a graph $G$ , let $τ (G)$ be the maximum number of colors such that there exists an edge-coloring of $G$ with no two color classes being isomorphic. We investigate the behavior o…

math.CO2022

The Erdős-Gyárfás function $f (n, 4, 5) = \frac{5}{6} n + o (n)$ -- so Gyárfás was right

Patrick Bennett, Ryan Cushman, Andrzej Dudek +1

A $(4, 5)$ -coloring of $K_{n}$ is an edge-coloring of $K_{n}$ where every $4$ -clique spans at least five colors. We show that there exist $(4, 5)$ -colorings of $K_{n}$ using $\frac 56 n…

math.CO2022

Powers of Hamiltonian cycles in randomly augmented Dirac graphs -- the complete collection

Sylwia Antoniuk, Andrzej Dudek, Andrzej Ruciński

We study the powers of Hamiltonian cycles in randomly augmented Dirac graphs, that is, $n$ -vertex graphs $G$ with minimum degree at least $(1/2 + ε) n$ to which some random…

Erdős-Szekeres type Theorems for ordered uniform matchings

A random coloring process gives improved bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers

Ordered unavoidable sub-structures in matchings and random matchings

A note on non-isomorphic edge-color classes in random graphs

The Erdős-Gyárfás function f(n,4,5)=65​n+o(n) -- so Gyárfás was right

Powers of Hamiltonian cycles in randomly augmented Dirac graphs -- the complete collection

The Erdős-Gyárfás function $f (n, 4, 5) = \frac{5}{6} n + o (n)$ -- so Gyárfás was right