J. Corsten

activity

20172021

most citedA note on the grid Ramsey problem

1 citations · 1 across the 1 of their papers we have counts for

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math.CO2021

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

Jan Corsten, Walner Mendonça

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

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

Partitioning infinite hypergraphs into few monochromatic Berge-paths

Sebastián Bustamante, Jan Corsten, Nóra 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.CO2019

Partitioning edge-coloured hypergraphs into few monochromatic tight cycles

Sebastián Bustamante, Jan Corsten, Nóra Frankl +2

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

math.CO2018

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.CO2017★ 1 cited

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 $Γ_{n, n} := K_{n} \times K_{n}$ with $r$ colours induces a rectangle whose…