Arsenii Sagdeev

activity

20242026

collaborators

7 papers

math.CO2026

Vertex-Ramsey theorems for Cartesian powers of graphs

Nóra Almási, Maria Axenovich, Arsenii Sagdeev

For graphs $G, H$ and positive integers $r$ and $n$ we write $G^{□ n} r H$ if every $r$ -vertex-coloring of the Cartesian power $G^{□ n}$ of $G$ contains a…

math.CO2026

Largest density of a layered subgraph of a hypercube

Maria Axenovich, Arsenii Sagdeev

Let $L (t)$ denote the largest number of edges induced by $t$ vertices from two vertex layers of a hypercube. We show that $$\frac14 t\log_2 t+\frac18 t\log_2\log_2 t-O(t) \leq L(t)…

math.CO2025

Ramsey problems for graphs in Euclidean spaces and Cartesian powers

Maria Axenovich, Dingyuan Liu, Arsenii Sagdeev

Given a graph $H$ , let $χ_{H} (R^{n})$ be the smallest positive integer $r$ such that there exists an $r$ -coloring of $R^{n}$ with no monochromatic unit-copy of $H$ , tha…

cs.DM2024

A Stopping Game on Zero-Sum Sequences

Adrian Dumitrescu, Arsenii Sagdeev

We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A = (a_{1}, \dots, a_{n})$ of a multiset $M$ of $n$ reals…

math.CO2024

Faces in girth-saturated graphs on surfaces

Maria Axenovich, Leon Kießle, Arsenii Sagdeev +1

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

math.CO2024

Packing Density of Sets With Only Two Nonmixed Gaps

Alexander Natalchenko, Arsenii Sagdeev

For a finite set of integers such that the first few gaps between its consecutive elements equal $a$ , while the remaining gaps equal $b$ , we study dense packings of its translates…