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