Maksim Zhukovskii

collaborators

4 papers

math.PR2025

On the threshold for triangulations inside convex polygons

Brett Kolesnik, Georgii Zakharov, Maksim Zhukovskii

Start with a large convex polygon and add all other edges inside independently with probability $p$ . At what critical threshold $p_{c}$ do triangulations of the polygon begin to appe…

math.CO2025

Sums along the edges of bounded degree graphs

Noga Alon, Itai Benjamini, Georgii Zakharov +1

Let $G$ be a graph on $n$ vertices and $(H, +)$ be an abelian group. What is the minimum size $S_{H} (G)$ of the set of all sums $A (u) + A (v)$ over all injections $A : V (G) \to H$ ? In…

math.CO2025

Majority dynamics on finite trees

Itai Benjamini, Georgii Zakharov, Maksim Zhukovskii

For an arbitrary finite tree $T$ , we find the exact value of the wort-case stabilisation time of majority dynamics on $T$ . We also prove that for a perfect rooted cubic tree $T$ wi…

math.CO2025

Faces in girth-saturated graphs on surfaces

Maria Axenovich, Leon KieÃle, Arsenii Sagdeev +1

What is the maximum length $f_{max} (ℓ, I^£)$ of a facial cycle of an inclusion-maximal graph with girth at least $ℓ$ embedded on a given surface $I^£$ ? If $Î£=\mathca…