A. Polyanskii

activity

20142023

most citedForbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines

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

collaborators

Showing 2016Show all

4 papers · 1 filter

math.MG2016

Helly-type theorem for eigenvectors

Alexandr Polyanskii

We prove that if any $⌊ 3 d /2 ⌋$ or fewer elements of a finite family of linear operators $K^{d} \to K^{d}$ ( $K$ is an arbitrary field) have a common e…

math.MG2016★ 9 cited

Pairwise intersecting homothets of a convex body

Alexandr Polyanskii

We show that the maximum number of pairwise intersecting positive homothets of a $d$ -dimensional centrally symmetric convex body, none of which contains the center of another in it…

math.CO2016★ 4 cited

Approximating set multi-covers

Márton Naszódi, Alexandr Polyanskii

Johnson and Lovász and Stein proved independently that any hypergraph satisfies $τ \leq (1 + ln Δ) τ^{*}$ , where $τ$ is the transversal number, $τ^{*}$ is its fractional version…

math.MG2016

On reduced polytopes

Alexandr Polyanskii

A convex body $R$ in $R^{d}$ is called reduced if the minimal width $Δ (R^{'})$ of each convex body $R^{'} \subset R$ different from $R$ is strictly smaller than the minimal width $Δ…