A. Polyanskii

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20232026

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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…

KKM meets colorful Carathéodory

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