Counterexamples to Borsuk's conjecture on spheres of small radius

DOI10.1134/S1064562410050108zbMath1217.52007OpenAlexW2964331463WikidataQ122859839 ScholiaQ122859839MaRDI QIDQ630237

Andrei M. Raigorodskii

Publication date: 17 March 2011

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562410050108

zbMATH Keywords

chromatic numberBorsuk problem

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Other problems of combinatorial convexity (52A37) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items (6)

An improvement of the Frankl-Wilson theorem on the number of edges in a hypergraph with forbidden intersections of edges ⋮ Realization of subgraphs of random graphs by graphs of diameters in Euclidean spaces ⋮ New estimates in the problem of the number of edges in a hypergraph with forbidden intersections ⋮ Zero-one law for random distance graphs with vertices in \(\{-1,0,1\}^n\) ⋮ On the realization of subgraphs of a random graph by diameter graphs in Euclidean spaces ⋮ New upper bounds for the independence numbers of graphs with vertices in \(\{-1,0,1\}^n\) and their applications to problems of the chromatic numbers of distance graphs

Cites Work

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• The Borsuk partition problem: the seventieth anniversary
• Excursions into combinatorial geometry
• Illuminating sets of constant width
• On the dimension in Borsuk's problem
• Drei Sätze über die n-dimensionale euklidische Sphäre

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