Patryk Morawski

activity

20242026

collaborators

5 papers

math.CO2026

Ramsey number of a cycle versus a graph of a given size

Stijn Cambie, Andrea Freschi, Patryk Morawski +2

In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R (C_{k}, H)$ is at most $2 m + ⌊ \frac{k - 1}{2} ⌋$ ,…

math.CO2025

Ramsey numbers of digraphs with local edge structure

Domagoj Bradač, Patryk Morawski, Benny Sudakov +1

One of the classical topics in graph Ramsey theory is the study of which $n$ -vertex graphs have Ramsey numbers that are linear in $n$ . In this paper, we consider this problem in th…

math.CO2025

Hamilton cycles in regular graphs perturbed by a random 2-factor

Cicely, Henderson, Sean Longbrake +2

In this paper, we prove that for each $d \geq 2$ , the union of a $d$ -regular graph with a uniformly random $2$ -factor on the same vertex set is Hamiltonian with high probability. T…

math.CO2024

Ordered Ramsey numbers of graphs with $m$ edges

Domagoj Bradač, Patryk Morawski, Benny Sudakov +1

Given a vertex-ordered graph $G$ , the ordered Ramsey number $r_{<} (G)$ is the minimum integer $N$ such that every $2$ -coloring of the edges of the complete ordered graph $K_{N}$ contai…

math.CO2024

Oriented Ramsey numbers of graded digraphs

Patryk Morawski, Yuval Wigderson

We show that any graded digraph $D$ on $n$ vertices with maximum degree $Δ$ has an oriented Ramsey number of at most $C^{Δ} n$ for some absolute constant $C > 1$ , improving upon a rec…