Sahar Diskin

activity

20212026

most citedPercolation on Irregular High-dimensional Product Graphs

3 citations · 6 across the 26 of their papers we have counts for

collaborators

Showing 2024Show all

9 papers · 1 filter

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

Minimum degree $k$ and $k$ -connectedness usually arrive together

Sahar Diskin, Anna Geisler

Let $d, n \in N$ be such that $d = ω (1)$ , and $d \leq n^{1 - a}$ for some constant $a > 0$ . Consider a $d$ -regular graph $G = (V, E)$ and the random graph process that starts with the…

math.CO2024

Components, large and small, are as they should be II: supercritical percolation on regular graphs of constant degree

Sahar Diskin, Michael Krivelevich

Let $d \geq 3$ be a fixed integer. Let $y := y (p)$ be the probability that the root of an infinite $d$ -regular tree belongs to an infinite cluster after $p$ -bond-percolation. We show…

math.CO2024

Components, large and small, are as they should be I: supercritical percolation on regular graphs of growing degree

Sahar Diskin, Michael Krivelevich

We provide sufficient conditions for a regular graph $G$ of growing degree $d$ , guaranteeing a phase transition in its random subgraph $G_{p}$ similar to that of $G (n, p)$ when $p\cdo…

math.CO2024

Large matchings and nearly spanning, nearly regular subgraphs of random subgraphs

Sahar Diskin, Joshua Erde, Mihyun Kang +1

Given a graph $G$ and $p \in [0, 1]$ , the random subgraph $G_{p}$ is obtained by retaining each edge of $G$ independently with probability $p$ . We show that for every $ε > 0$ , there exis…

math.CO2024

Long cycles in percolated expanders

Maurício Collares, Sahar Diskin, Joshua Erde +1

Given a graph $G$ and probability $p$ , we form the random subgraph $G_{p}$ by retaining each edge of $G$ independently with probability $p$ . Given $d \in N$ and constants $0<c…

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.PR2024

Hitting time of connectedness in the random hypercube process

Sahar Diskin, Michael Krivelevich

We present a short and self-contained proof of a classical result due to Bollobás (1990): in the random hypercube process, with high probability the hitting time of connectedness e…

math.CO2024

Perfect Matching in Product Graphs and in their Random Subgraphs

Sahar Diskin, Anna Geisler

For $t \in N$ and ever $i \in [t]$ , let $H_{i}$ be a $d_{i}$ -regular connected graph with $1 < ∣ V (H_{i}) ∣ \leq M$ for some integer $M \geq 2$ . Let $G = □_{i = 1}^{t} H_{i}$ be the $t$ -dime…

Tree tilings in random regular graphs

Minimum degree k and k-connectedness usually arrive together

Components, large and small, are as they should be II: supercritical percolation on regular graphs of constant degree

Components, large and small, are as they should be I: supercritical percolation on regular graphs of growing degree

Large matchings and nearly spanning, nearly regular subgraphs of random subgraphs

Long cycles in percolated expanders

Saturation in Random Hypergraphs

Hitting time of connectedness in the random hypercube process

Perfect Matching in Product Graphs and in their Random Subgraphs

Minimum degree $k$ and $k$ -connectedness usually arrive together