Michael Anastos

activity

20162025

most citedHamiltonicity of random graphs in the stochastic block model

3 citations · 11 across the 32 of their papers we have counts for

collaborators

38 papers

math.PR2025

Diameter and mixing time of the giant component in the percolated hypercube

Michael Anastos, Sahar Diskin, Lyuben Lichev +1

We consider bond percolation on the $d$ -dimensional binary hypercube with $p = c / d$ for fixed $c > 1$ . We prove that the typical diameter of the giant component $L_{1}$ is of order $Θ(d)…

math.CO2025

Optimally building spanning graphs in semirandom graph processes

Michael Anastos, Maurício Collares, Joshua Erde +3

The semirandom graph process constructs a graph $G$ in a series of rounds, starting with the empty graph on $n$ vertices. In each round, a player is offered a vertex $v$ chosen uni…

math.CO2025

Cycle lengths in the percolated hypercube

Michael Anastos, Sahar Diskin, Joshua Erde +3

Let $Q_{p}^{d}$ be the random subgraph of the $d$ -dimensional binary hypercube obtained after edge-percolation with probability $p$ . It was shown recently by the authors that, for ever…

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.CO2025

The law of the circumference of sparse binomial random graphs

Michael Anastos, Joshua Erde, Mihyun Kang +1

There has been much interest in the distribution of the circumference, the length of the longest cycle, of a random graph $G (n, p)$ in the sparse regime, when $p = Θ\left(\frac{1}{n…