skip to main content

SciTech ConnectSciTech Connect

Title: Covering sets in R{sup m}

The paper investigates questions related to Borsuk's classical problem of partitioning a set in Euclidean space into subsets of smaller diameter, as well as to the well-known Nelson-Erdős-Hadwiger problem on the chromatic number of a Euclidean space. The results of the work are obtained using combinatorial and geometric methods alike. A new approach to the investigation of such problems is suggested; it leads to a collection of results which significantly improve all results known so far. Bibliography: 58 titles.
Authors:
 [1]
  1. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region (Russian Federation)
Publication Date:
OSTI Identifier:
22364913
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 8; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; EUCLIDEAN SPACE; GEOMETRY; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS