Sahar Diskin

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math.CO2025

Spanning trees of bounded degree in random geometric graphs

Michael Anastos, Sahar Diskin, Dawid Ignasiak +2

We determine the sharp threshold for the containment of all $n$ -vertex trees of bounded degree in random geometric graphs with $n$ vertices. This provides a geometric counterpart o…

math.CO2025

Nearly spanning cycle in the percolated hypercube

Michael Anastos, Sahar Diskin, Joshua Erde +3

Let $Q^{d}$ be the $d$ -dimensional binary hypercube. We form a random subgraph $Q_{p}^{d} \subseteq Q^{d}$ by retaining each edge of $Q^{d}$ independently with probability $p$ . We show that,…

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…