Ilay Hoshen

activity

20222026

most citedSimonovits's theorem in random graphs

1 citations · 1 across the 7 of their papers we have counts for

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9 papers · 1 filter

math.CO2026

A Local Central Limit Theorem for Clique Counts in Sparse Random Graphs

Asaf Cohen Antonir, Ilay Hoshen, Maksim Zhukovskii

Let $X_{H}$ denote the number of copies of a fixed graph $H$ in $G_{n, p}$ . Gilmer and Kopparty conjectured that $X_{H}$ satisfies a local central limit theorem (LCLT) provided that $H…

math.CO2026

Optimal lower bounds for epsilon-nets for lines in the plane

Ilay Hoshen, Wojciech Samotij

We prove that, for arbitrarily small positive $ε$ , there is a finite planar point set $P$ such that every $ε$ -net for the range space induced on $P$ by straight…

math.CO2026

Random Turán Theorem for the Fano Plane

Ilay Hoshen

Let $F$ denote the Fano plane, the $3$ -uniform hypergraph with $7$ vertices and $7$ edges. Frankl and Füredi, and independently Keevash and Sudakov, proved that the largest $F$ -fre…

math.CO2024

Tree tilings in random regular graphs

Sahar Diskin, Ilay Hoshen, Maksim Zhukovskii

We show that for every $ε > 0$ there exists a sufficiently large $d_{0} \in N$ such that for every $d \geq d_{0}$ , whp the random $d$ -regular graph $G (n, d)$ contains a $T$ -factor f…

math.CO2024

Saturation in Random Hypergraphs

Sahar Diskin, Ilay Hoshen, Dániel Korándi +2

Let $K_{n}^{r}$ be the complete $r$ -uniform hypergraph on $n$ vertices, that is, the hypergraph whose vertex set is $[n] := {1, 2, ..., n}$ and whose edge set is $(r [ n ])$ . We form…

math.CO2024

Stability of large cuts in random graphs

Ilay Hoshen, Wojciech Samotij, Maksim Zhukovskii

We prove that the family of largest cuts in the binomial random graph exhibits the following stability property: If $1/ n ≪ p = 1 - Ω (1)$ , then, with high probability, there is a se…

math.CO2023★ 1 cited

Simonovits's theorem in random graphs

Ilay Hoshen, Wojciech Samotij

Let $H$ be a graph with $χ (H) = r + 1$ . Simonovits's theorem states that, if $H$ is edge-critical, the unique largest $H$ -free subgraph of $K_{n}$ is its largest $r$ -partite subgraph,…

math.CO2023

A Jump of the Saturation Number in Random Graphs?

Sahar Diskin, Ilay Hoshen, Maksim Zhukovskii

For graphs $G$ and $F$ , the saturation number $sat (G, F)$ is the minimum number of edges in an inclusion-maximal $F$ -free subgraph of $G$ . In 2017, Korándi and Sudakov init…

math.CO2022

On vertex Ramsey graphs with forbidden subgraphs

Sahar Diskin, Ilay Hoshen, Michael Krivelevich +1

A classical vertex Ramsey result due to Nešetřil and Rödl states that given a finite family of graphs $F$ , a graph $A$ and a positive integer $r$ , if every graph $B\in\ma…