István Tomon

activity

20142026

most citedOn the Turán number of some ordered even cycles

10 citations · 38 across the 54 of their papers we have counts for

collaborators

Showing 2022Show all

8 papers · 1 filter

math.CO2022

Lower bounds for piercing and coloring boxes

István Tomon

Given a family $B$ of axis-parallel boxes in $R^{d}$ , let $τ$ denote its piercing number, and $ν$ its independence number. It is an old question whether $τ / ν$ can…

math.CO2022

Regular subgraphs of linear hypergraphs

Oliver Janzer, Benny Sudakov, István Tomon

We prove that the maximum number of edges in a 3-uniform linear hypergraph on $n$ vertices containing no 2-regular subhypergraph is $n^{1 + o (1)}$ . This resolves a conjecture of Dell…

math.CO2022

Ramsey numbers of semi-algebraic and semi-linear hypergraphs

Zhihan Jin, István Tomon

An $r$ -uniform hypergraph $H$ is semi-algebraic of complexity $t = (d, D, m)$ if the vertices of $H$ correspond to points in $R^{d}$ , and the edges of $H$ are determi…

math.CO2022

Evasive sets, covering by subspaces, and point-hyperplane incidences

Benny Sudakov, István Tomon

Given positive integers $k \leq d$ and a finite field $F$ , a set $S \subset F^{d}$ is $(k, c)$ -subspace evasive if every $k$ -dimensional affine subspace contains at m…

math.CO2022

Small subgraphs with large average degree

Oliver Janzer, Benny Sudakov, István Tomon

In this paper we study the fundamental problem of finding small dense subgraphs in a given graph. For a real number $s > 2$ , we prove that every graph on $n$ vertices with average de…

math.CO2022

Irredundant hyperplane covers

János Nagy, Péter Pál Pach, István Tomon

We prove that if $G$ is an abelian group and $H_{1} x_{1}, \dots, H_{k} x_{k}$ is an irredundant (minimal) cover of $G$ with cosets, then $∣ G : i = 1 ⋂ k H_{i} ∣ = 2^{O (k)} .$ This bound…

math.CO2022

The Turán number of the grid

Domagoj Bradač, Oliver Janzer, Benny Sudakov +1

For a positive integer $t$ , let $F_{t}$ denote the graph of the $t \times t$ grid. Motivated by a 50-year-old conjecture of Erdős about Turán numbers of $r$ -degenerate graphs, we prov…

math.CO2022★ 7 cited

Robust (rainbow) subdivisions and simplicial cycles

István Tomon

We present several results in extremal graph and hypergraph theory of topological nature. First, we show that if $α > 0$ and $ℓ = Ω (\frac{1}{α} lo g \frac{1}{α})$ is an odd integer, then…