Michael Anastos

activity

20242026

collaborators

11 papers

math.CO2026

A note on finding large transversals efficiently

Michael Anastos, Patrick Morris

In an $n \times n$ array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more…

math.PR2026

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 $Î(d…

math.CO2026

Robust Hamiltonicity in families of Dirac graphs

Michael Anastos, Debsoumya Chakraborti

A graph is called Dirac if its minimum degree is at least half of the number of vertices in it. Joos and Kim showed that every collection $G = {G_{1}, \dots, G_{n}}$ of Dirac g…

math.CO2025

Optimally building spanning graphs in semirandom graph processes

Michael Anastos, MaurÃcio 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…