Nóra Frankl

activity

20162023

most citedEmbedding graphs in Euclidean space

12 citations · 35 across the 12 of their papers we have counts for

collaborators

17 papers

math.CO2023★ 2 cited

Monochromatic infinite sets in Minkowski planes

Nóra Frankl, Panna Gehér, Arsenii Sagdeev +1

We prove that for any $ℓ_{p}$ -norm in the plane with $1 < p < \infty$ and for every infinite $M \subset R^{2}$ , there exists a two-colouring of the plane such that no…

math.CO2023★ 1 cited

Graphs with large minimum degree and no small odd cycles are $3$ -colourable

Julia Böttcher, Nóra Frankl, Domenico Mergoni Cecchelli +2

Answering a question by Letzter and Snyder, we prove that for large enough $k$ any $n$ -vertex graph $G$ with minimum degree at least $\frac{1}{2 k - 1} n$ and without odd cycles of len…

math.CO2023

On Helly numbers of exponential lattices

Gergely Ambrus, Martin Balko, Nóra Frankl +2

Given a set $S \subseteq R^{2}$ , define the \emph{Helly number of $S$ }, denoted by $H (S)$ , as the smallest positive integer $N$ , if it exists, for which the following statem…

math.CO2022★ 5 cited

Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings

Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev

In 2008, Schmidt and Tuller stated a conjecture concerning optimal packing and covering of integers by translates of a given three-point set. In this note, we confirm their conject…

math.CO2022

On some non-rigid unit distance patterns

Nora Frankl, Dora Woodruff

A recent generalization of the Erdős Unit Distance Problem, proposed by Palsson, Senger and Sheffer, asks for the maximum number of unit distance paths with a given number of verti…

math.CO2021

On the Erdős-Purdy problem and the Zarankiewitz problem for semialgebraic graphs

Nora Frankl, Andrey Kupavskii

Erdős and Purdy, and later Agarwal and Sharir, conjectured that any set of $n$ points in $R^{d}$ determine at most $C n^{d /2}$ congruent $k$ -simplices for even $d$ . We obtai…

math.CO2021★ 2 cited

Max-norm Ramsey Theory

Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev

Given a metric space $M$ that contains at least two points, the chromatic number $χ (R_{\infty}^{n}, M)$ is defined as the minimum number of c…

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-monochromatic sets and the chromatic number of the plane

Nóra Frankl, Tamás Hubai, Dömötör Pálvölgyi

In a colouring of $R^{d}$ a pair $(S, s_{0})$ with $S \subseteq R^{d}$ and with $s_{0} \in S$ is \emph{almost monochromatic} if $S ∖ {s_{0}}$ is monochromatic but $S$ …

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

Nearly $k$ -distance sets

Nóra Frankl, Andrey Kupavskii

We say that a set of points $S \subset R^{d}$ is an $ε$ -nearly $k$ -distance set if there exist $1 \leq t_{1} \leq \dots \leq t_{k},$ such that the distance between any two d…

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★ 10 cited

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★ 12 cited

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…

math.CO2017★ 1 cited

A note on diameter-Ramsey sets

Jan Corsten, Nóra 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.MG2016★ 2 cited

Coverings: variations on a result of Rogers and on the Epsilon-net theorem of Haussler and Welzl

Nóra Frankl, János Nagy, Márton Naszódi

We consider four problems. Rogers proved that for any convex body $K$ , we can cover $R^{d}$ by translates of $K$ of density very roughly $d ln d$ . First, we extend this res…

Monochromatic infinite sets in Minkowski planes

Graphs with large minimum degree and no small odd cycles are 3-colourable

On Helly numbers of exponential lattices

Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings

On some non-rigid unit distance patterns

On the Erdős-Purdy problem and the Zarankiewitz problem for semialgebraic graphs

Max-norm Ramsey Theory

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

VC-saturated set systems

Almost-monochromatic sets and the chromatic number of the plane

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

Nearly k-distance sets

Partitioning infinite hypergraphs into few monochromatic Berge-paths

Partitioning edge-coloured hypergraphs into few monochromatic tight cycles

Embedding graphs in Euclidean space

A note on diameter-Ramsey sets

Coverings: variations on a result of Rogers and on the Epsilon-net theorem of Haussler and Welzl

Graphs with large minimum degree and no small odd cycles are $3$ -colourable

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

Nearly $k$ -distance sets