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papers

Publications (10)

math.CO2020

Partitioning edge-coloured hypergraphs into few monochromatic tight cycles

SebastiÃ¡n Bustamante, Jan Corsten, NÃ³ra Frankl +2

Confirming a conjecture of GyÃ¡rfÃ¡s, we prove that, for all natural numbers $k$ and $r$ , the vertices of every $r$ -edge-coloured complete $k$ -uniform hypergraph can be partitioned…

math.CO2019

On the Odd Cycle Game and Connected Rules

Jan Corsten, Adva Mond, Alexey Pokrovskiy +2

We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_{n}$ . Maker wins if she succeeds in cl…

math.CO2019

Upper density of monochromatic infinite paths

Jan Corsten, Louis DeBiasio, Ander Lamaison +1

We prove that in every $2$ -colouring of the edges of $K_{N}$ there exists a monochromatic infinite path $P$ such that $V (P)$ has upper density at least ${(12+\sqrt{8})}/{17}…

math.CO2019

Partitioning infinite hypergraphs into few monochromatic Berge-paths

SebastiÃ¡n Bustamante, Jan Corsten, NÃ³ra Frankl

Extending a result of Rado to hypergraphs, we prove that for all $s, k, t \in N$ with $k \geq t \geq 2$ , the vertices of every $r = s (k - t + 1)$ -edge-coloured countably infin…

math.CO2018

A note on diameter-Ramsey sets

Jan Corsten, NÃ³ra Frankl

A finite set $A \subset R^{d}$ is called $diameter-Ramsey$ if for every $r \in N$ , there exists some $n \in N$ and a finite set $B \subset \mathbb{R…

math.CO2022

Balanced supersaturation for some degenerate hypergraphs

Jan Corsten, Tuan Tran

A classical theorem of Simonovits from the 1980s asserts that every graph $G$ satisfying $e (G) ≫ v (G)^{1 + 1/ k}$ must contain $≳ (\frac{e ( G )}{v ( G )})^{2 k}$ copies…

math.CO2021

Tiling edge-coloured graphs with few monochromatic bounded-degree graphs

Jan Corsten, Walner MendonÃ§a

We prove that for all integers $I^, r \geq 2$ , there is a constant $C = C (I^, r) > 0$ such that the following is true for every sequence $F = {F_{1}, F_{2}, \dots}$ of graphs…

math.CO2017

A note on the grid Ramsey problem

Jan Corsten

The grid Ramsey number $G (r)$ is the smallest number $n$ such that every edge-colouring of the grid graph $I^_{n, n} := K_{n} \times K_{n}$ with $r$ colours induces a rectangle whos…

math.CO2025

Density of monochromatic infinite subgraphs II

Jan Corsten, Louis DeBiasio, Paul McKenney

In 1967, GerencsÃ©r and GyÃ¡rfÃ¡s proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_{n}$ there is a monochromatic path on $\lce…

math.CO2026

A robust CorrÃ¡di--Hajnal Theorem

Peter Allen, Julia BÃ¶ttcher, Jan Corsten +5

For a graph $G$ and $p \in [0, 1]$ , we denote by $G_{p}$ the random sparsification of $G$ obtained by keeping each edge of $G$ independently, with probability $p$ . We show that there ex…