A. Polyanskii

activity

20232026

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5 papers · 1 filter

math.CO2026

KKM meets colorful Carathéodory

Alexander Polyanskii

The colorful Carathéodory theorem states that if $V_{1}, \dots, V_{d + 1} \subset R^{d}$ satisfy $0 \in conv V_{i}$ for every $i$ , then there exist points $v_{i} \in V_{i}$ such tha…

math.CO2026

Spanning $k$-trees and the colorful Carathéodory theorem

Mikhail Bludov, Alexander Polyanskii

Very recently, using Meshulam's lemma, Blagojević proved a constrained version of the colorful Carathéodory theorem for joins of bipartite spanning trees and wedge of spheres. Our…

math.CO2025

New Helly-type results for discrete boxes: Quantitative colorful and $(p, q)$ -variants

Rahul Gangopadhyay, Alexander Polyanskii, Wei Rao

In 2008, Halman showed that for any finite set $P \subset R^{d}$ and any finite family $B$ of axis-parallel boxes in $R^{d}$ , if the intersection of $P$ and a…

math.CO2025

No-dimensional Tverberg-type problems

Alexander Polyanskii

Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given $n \geq k$ , partition…

math.CO2023

Alon-Boppana-type bounds for weighted graphs

Alexandr Polyanskii, Rinat Sadykov

The unraveled ball of radius $r$ centered at a vertex $v$ in a weighted graph $G$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$ . We present a general boun…

KKM meets colorful Carathéodory

Spanning \(k\)-trees and the colorful Carathéodory theorem

New Helly-type results for discrete boxes: Quantitative colorful and (p,q)-variants

No-dimensional Tverberg-type problems

Alon-Boppana-type bounds for weighted graphs

New Helly-type results for discrete boxes: Quantitative colorful and $(p, q)$ -variants