Search Results - "Diskin, Sahar"

Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs by Diskin, Sahar, Erde, Joshua, Kang, Mihyun, Krivelevich, Michael

“…It is known that many different types of finite random subgraph models undergo quantitatively similar phase transitions around their percolation thresholds,…”
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Expansion in supercritical random subgraphs of expanders and its consequences by Diskin, Sahar, Krivelevich, Michael

“…In 2004, Frieze, Krivelevich and Martin established the emergence of a giant component in random subgraphs of pseudo‐random graphs. We study several typical…”
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Heavy and light paths and Hamilton cycles by Diskin, Sahar, Elboim, Dor

“…Given a graph G, we denote by f(G,u0,k) the number of paths of length k in G starting from u0. In graphs of maximum degree 3, with edge weights i.i.d. with…”
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Site percolation on pseudo‐random graphs by Diskin, Sahar, Krivelevich, Michael

“…We consider vertex percolation on pseudo‐random d$$ d $$‐regular graphs. The previous study by the second author established the existence of phase transition…”
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On the Performance of the Depth First Search Algorithm in Supercritical Random Graphs by Diskin, Sahar, Krivelevich, Michael

“…We consider the performance of the Depth First Search (DFS) algorithm on the random graph $G\left(n,\frac{1+\epsilon}{n}\right)$, $\epsilon>0$ a small…”
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Percolation on High‐Dimensional Product Graphs by Diskin, Sahar, Erde, Joshua, Kang, Mihyun, Krivelevich, Michael

“…We consider percolation on high‐dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show that…”
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On vertex Ramsey graphs with forbidden subgraphs by Diskin, Sahar, Hoshen, Ilay, Krivelevich, Michael, Zhukovskii, Maksim

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Climbing up a random subgraph of the hypercube by Anastos, Michael, Diskin, Sahar, Elboim, Dor, Krivelevich, Michael

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Minimum degree $k$ and $k$-connectedness usually arrive together by Diskin, Sahar, Geisler, Anna

“…Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph…”
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Components, large and small, are as they should be I: supercritical percolation on regular graphs of growing degree by Diskin, Sahar, Krivelevich, Michael

“…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…”
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Components, large and small, are as they should be II: supercritical percolation on regular graphs of constant degree by Diskin, Sahar, Krivelevich, Michael

“…Let $d\ge 3$ 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…”
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Isoperimetry in product graphs by Diskin, Sahar, Samotij, Wojciech

“…In this short note, we establish an edge-isoperimetric inequality for arbitrary product graphs. Our inequality is sharp for subsets of many different sizes in…”
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Perfect Matching in Product Graphs and in their Random Subgraphs by Diskin, Sahar, Geisler, Anna

“…For $t \in \mathbb{N}$ and every $i\in[t]$, let $H_i$ be a $d_i$-regular connected graph, with $1<|V(H_i)|\le C$ for some integer $C\ge 2$. Let…”
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Hitting time of connectedness in the random hypercube process by Diskin, Sahar, Krivelevich, Michael

“…We present a short and self-contained proof of a classical result due to Bollob\'as (1990): in the random hypercube process, with high probability the hitting…”
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Heavy and Light Paths and Hamilton Cycles by Diskin, Sahar, Elboim, Dor

“…Given a graph $G$, we denote by $f(G,u_0,k)$ the number of paths of length $k$ in $G$ starting from $u_0$. In graphs of maximum degree 3, with edge weights…”
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Expansion in Supercritical Random Subgraphs of Expanders and its Consequences by Diskin, Sahar, Krivelevich, Michael

“…In 2004, Frieze, Krivelevich and Martin [17] established the emergence of a giant component in random subgraphs of pseudo-random graphs. We study several…”
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Supercritical Site Percolation on the Hypercube: Small Components are Small by Diskin, Sahar, Krivelevich, Michael

“…We consider supercritical site percolation on the $d$-dimensional hypercube $Q^d$. We show that typically all components in the percolated hypercube, besides…”
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On the Performance of the Depth First Search Algorithm in Supercritical Random Graphs by Diskin, Sahar, Krivelevich, Michael

“…We consider the performance of the Depth First Search (DFS) algorithm on the random graph $G\left(n,\frac{1+\epsilon}{n}\right)$, $\epsilon>0$ a small…”
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Site Percolation on Pseudo-Random Graphs by Diskin, Sahar, Krivelevich, Michael

“…We consider vertex percolation on pseudo-random $d-$regular graphs. The previous study by the second author established the existence of phase transition from…”
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A Jump of the Saturation Number in Random Graphs? by Diskin, Sahar, Hoshen, Ilay, Zhukovskii, Maksim

“…For graphs $G$ and $F$, the saturation number $\textit{sat}(G,F)$ is the minimum number of edges in an inclusion-maximal $F$-free subgraph of $G$. In 2017,…”
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