Arsenii Sagdeev

activity

20202026

most citedAll finite sets are Ramsey in the maximum norm

12 citations · 35 across the 18 of their papers we have counts for

collaborators

18 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…

math.CO2024

Maximizing the Maximum Degree in Ordered Nearest Neighbor Graphs

Péter Ágoston, Adrian Dumitrescu, Arsenii Sagdeev +2

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.CO2024

Canonical theorems in geometric Ramsey theory

Panna Gehér, Arsenii Sagdeev, Géza Tóth

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…

math.CO2024★ 1 cited

General penny graphs are at most 43/18-dense

Arsenii Sagdeev

We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43 n /18$ times, improving upon the upper bound of $17 n /7$ obtained by Tóth in…

math.CO2023★ 2 cited

Monochromatic infinite sets in Minkowski planes

Nóra Frankl, Panna Gehér, Arsenii Sagdeev +1

We prove that for any $ℓ_{p}$ -norm in the plane with $1 < p < \infty$ and for every infinite $M \subset R^{2}$ , there exists a two-colouring of the plane such that no…

math.MG2023★ 4 cited

A note on Borsuk's problem in Minkowski spaces

Andrei M. Raigorodskii, Arsenii Sagdeev

In 1993, Kahn and Kalai famously constructed a sequence of finite sets in $d$ -dimensional Euclidean spaces that cannot be partitioned into less than $(1.203 \dots + o (1))^{d}$ …

math.CO2023

Monochromatic triangles in the max-norm plane

Alexander Natalchenko, Arsenii Sagdeev

For all non-degenerate triangles T, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of T is monochromatic.

math.CO2022★ 1 cited

Cutting corners

Andrey Kupavskii, Arsenii Sagdeev, Dmitrii Zakharov

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

math.NT2022★ 1 cited

On the sequence $n! mod p$

A. Grebennikov, A. Sagdeev, A. Semchankau +1

We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(2 + o (1)) p$ distinct residues modulo prime $p$ . Moreover, factorials on an interval $\mathcal{I} \…

math.CO2022★ 5 cited

Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings

Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev

In 2008, Schmidt and Tuller stated a conjecture concerning optimal packing and covering of integers by translates of a given three-point set. In this note, we confirm their conject…

math.MG2022★ 7 cited

Odd-distance and right-equidistant sets in the maximum and Manhattan metrics

Alexander Golovanov, Andrey Kupavskii, Arsenii Sagdeev

We solve two related extremal-geometric questions in the $n -$ dimensional space $R_{\infty}^{n}$ equipped with the maximum metric. First, we prove that the maximum size of a…

math.CO2021★ 2 cited

Max-norm Ramsey Theory

Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev

Given a metric space $M$ that contains at least two points, the chromatic number $χ (R_{\infty}^{n}, M)$ is defined as the minimum number of c…

math.CO2020★ 12 cited

All finite sets are Ramsey in the maximum norm

Andrey Kupavskii, Arsenii Sagdeev

For two metric spaces $X$ and $Y$ , the chromatic number $χ (X; Y)$ of $X$ with forbidden $Y$ is the smallest $k$ such that there is…

Vertex-Ramsey theorems for Cartesian powers of graphs

Largest density of a layered subgraph of a hypercube

Ramsey problems for graphs in Euclidean spaces and Cartesian powers

A Stopping Game on Zero-Sum Sequences

Faces in girth-saturated graphs on surfaces

Packing Density of Sets With Only Two Nonmixed Gaps

Maximizing the Maximum Degree in Ordered Nearest Neighbor Graphs

Canonical theorems in geometric Ramsey theory

General penny graphs are at most 43/18-dense

Monochromatic infinite sets in Minkowski planes

A note on Borsuk's problem in Minkowski spaces

Monochromatic triangles in the max-norm plane

Cutting corners

On the sequence n!modp

Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings

Odd-distance and right-equidistant sets in the maximum and Manhattan metrics

Max-norm Ramsey Theory

All finite sets are Ramsey in the maximum norm

On the sequence $n! mod p$