Nóra Frankl

activity

20182020

collaborators

6 papers

math.CO2020

Large equilateral sets in subspaces of $ℓ_{\infty}^{n}$ of small codimension

Nora Frankl

For fixed $k$ we prove exponential lower bounds on the equilateral number of subspaces of $ℓ_{\infty}^{n}$ of codimension $k$ . In particular, we show that if the unit ball of a no…

math.CO2020

VC-saturated set systems

Nóra Frankl, Sergei Kiselev, Andrey Kupavskii +1

The well-known Sauer lemma states that a family $F \subseteq 2^{[n]}$ of VC-dimension at most $d$ has size at most $\sum_{i = 0}^{d} (i n)$ . We obtain both random and ex…

math.CO2019

Almost sharp bounds on the number of discrete chains in the plane

Nora Frankl, Andrey Kupavskii

The following generalisation of the Erdős unit distance problem was recently suggested by Palsson, Senger and Sheffer. Given $k$ positive real numbers $δ_{1}, \dots, δ_{k}$ , a $(k + 1)$ -tu…

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

Embedding graphs in Euclidean space

Nóra Frankl, Andrey Kupavskii, Konrad J. Swanepoel

The dimension of a graph $G$ is the smallest $d$ for which its vertices can be embedded in $d$ -dimensional Euclidean space in the sense that the distances between endpoints of edge…

Large equilateral sets in subspaces of ℓ∞n​ of small codimension

VC-saturated set systems

Almost sharp bounds on the number of discrete chains in the plane

Partitioning infinite hypergraphs into few monochromatic Berge-paths

Partitioning edge-coloured hypergraphs into few monochromatic tight cycles

Embedding graphs in Euclidean space

Large equilateral sets in subspaces of $ℓ_{\infty}^{n}$ of small codimension