27 citations · 83 across the 20 of their papers we have counts for
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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…
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 $…
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 $\…
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…