27 citations · 83 across the 20 of their papers we have counts for
21 papers
Intersecting diametral balls induced by a geometric graph II
Polina Barabanshchikova, Alexandr Polyanskii
For a graph whose vertices are points in , consider the closed balls with diameters induced by its edges. The graph is called a Tverberg graph if these closed balls in…
Intersecting ellipses induced by a max-sum matching
Polina Barabanshchikova, Alexandr Polyanskii
For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum…
Covering by planks and avoiding zeros of polynomials
Alexey Glazyrin, Roman Karasev, Alexandr Polyanskii
We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex…
Forbidden induced subgraphs for graphs and signed graphs with eigenvalues bounded from below
Zilin Jiang, Alexandr Polyanskii
The smallest eigenvalue of a graph is the smallest eigenvalue of its adjacency matrix. We show that the family of graphs with smallest eigenvalue at least can be defined by a…
Disjoint edges in geometric graphs
Nikita Chernega, Alexandr Polyanskii, Rinat Sadykov
A geometric graph is a graph drawn in the plane so that its vertices and edges are represented by points in general position and straight line segments, respectively. A vertex of a…
Intersecting diametral balls induced by a geometric graph
Olimjoni Pirahmad, Alexandr Polyanskii, Alexey Vasilevskii
For a graph whose vertex set is a finite set of points in the Euclidean -space consider the closed (open) balls with diameters induced by its edges. The graph is called a (an op…
The extremal number of surfaces
Andrey Kupavskii, Alexandr Polyanskii, István Tomon +1
In 1973, Brown, Erdős and Sós proved that if is a 3-uniform hypergraph on vertices which contains no triangulation of the sphere, then has at most $…
A cap covering theorem
Alexandr Polyanskii
A cap of spherical radius on a unit -sphere is the set of points within spherical distance from a given point on the sphere. Let be a finite set of caps…
Approximation of the average of some random matrices
Grigory Ivanov, Márton Naszódi, Alexandr Polyanskii
Rudelson's theorem states that if for a set of unit vectors and positive weights , we have that is the identity operator on …
Perron and Frobenius meet Carathéodory
Márton Naszódi, Alexandr Polyanskii
We present a new approach of proving certain Carathéodory-type theorems using the Perron-Frobenius Theorem, a classical result in matrix theory describing the largest eigenvalue of…
Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines
Zilin Jiang, Alexandr Polyanskii
The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let be the family of connected graphs of spectral radius . We show that $\…
On almost-equidistant sets - II
Alexandr Polyanskii
A set in is called almost-equidistant if for any three distinct points in the set, some two are at unit distance apart. First, we give a short proof of the result of…
On almost-equidistant sets
Alexandr Polyanskii
A finite set of points in is called almost-equidistant if among any three distinct points in the set, some two are at unit distance. We prove that an almost-equidista…
Proof of László Fejes Tóth's zone conjecture
Zilin Jiang, Alexandr Polyanskii
A zone of width on the unit sphere is the set of points within spherical distance of a given great circle. We show that the total width of any collection of zones coverin…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Alexandr Polyanskii +1
We show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in -di…
Helly-type theorem for eigenvectors
Alexandr Polyanskii
We prove that if any or fewer elements of a finite family of linear operators ( is an arbitrary field) have a common e…
Pairwise intersecting homothets of a convex body
Alexandr Polyanskii
We show that the maximum number of pairwise intersecting positive homothets of a -dimensional centrally symmetric convex body, none of which contains the center of another in it…
Approximating set multi-covers
Márton Naszódi, Alexandr Polyanskii
Johnson and Lovász and Stein proved independently that any hypergraph satisfies , where is the transversal number, is its fractional version…
On reduced polytopes
Alexandr Polyanskii
A convex body in is called reduced if the minimal width of each convex body different from is strictly smaller than the minimal width $Δ…
On the irrationality measure of certain numbers
Alexandr Polyanskii
The paper presents upper estimates for the irrationality measure and the non-quadraticity measure for the numbers $α_k=\sqrt{2k+1}\ln\frac{\sqrt{2k+1}-1}{\sqrt{2k+1}+1}, \ k\in\mat…
Proof of Schur's conjecture in
Andrey B. Kupavskii, Alexandr Polyanskii
In this paper we prove Schur's conjecture in , which states that any diameter graph in the Euclidean space on vertices may have at most cliqu…