Oliver Janzer

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20182025

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4 papers · 1 filter

math.CO2025

An improved upper bound for the multicolour Ramsey number of odd cycles

Maria Axenovich, Wouter Cames van Batenburg, Oliver Janzer +2

We show that the $k$ -colour Ramsey number of an odd cycle of length $2 ℓ + 1$ is at most $(4 ℓ)^{k} \cdot k^{k / ℓ}$ . This proves a conjecture of Fox and is the first improvem…

math.CO2019

The extremal number of the subdivisions of the complete bipartite graph

Oliver Janzer

For a graph $F$ , the $k$ -subdivision of $F$ , denoted $F^{k}$ , is the graph obtained by replacing the edges of $F$ with internally vertex-disjoint paths of length $k$ . In this paper,…

math.CO2019

The extremal number of longer subdivisions

Oliver Janzer

For a multigraph $F$ , the $k$ -subdivision of $F$ is the graph obtained by replacing the edges of $F$ with pairwise internally vertex-disjoint paths of length $k + 1$ . Conlon and Lee…

math.CO2018

Improved bounds for the extremal number of subdivisions

Oliver Janzer

Let $H_{t}$ be the subdivision of $K_{t}$ . Very recently, Conlon and Lee have proved that for any integer $t \geq 3$ , there exists a constant $C$ such that $\text{ex}(n,H_t)\leq Cn^{3/2…