Arsenii Sagdeev

activity

20242026

collaborators

9 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.CO2026

Cutting corners

Andrey Kupavskii, Arsenii Sagdeev, Dmitrii Zakharov

We say that a subset $M$ of $R^{n}$ is exponentially Ramsey if there are $I^µ > 0$ and $n_{0}$ such that $I ¨ (R^{n}, M) \geq (1 + I^µ)^{n}$ for any $n > n_{0}$ , where $I ¨ (R^{n}, M)$ …

math.CO2025

Ramsey problems for graphs in Euclidean spaces and Cartesian powers

Maria Axenovich, Dingyuan Liu, Arsenii Sagdeev

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

math.CO2025

Maximizing the Maximum Degree in Ordered Nearest Neighbor Graphs

For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to it…

math.CO2025

Canonical theorems in geometric Ramsey theory

In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical…