Uniform distances in rational unit-distance graphs

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Let G be the graph obtained from all the rational points in the d-space Ed by connecting every pair at Euclidean distance one. It is known that G is a connected graph, provided d ≥ 5. We establish an inequality of the form distG(x, y) ≤ ⌈|x - y|⌉ + 1, for all d ≥ 8, between the Euclidean distance |x - y| of any two rational points x and y and their corresponding distance distG(x, y) in the graph G. A slightly weaker relation is shown to hold in dimensions 5, 6 and 7.

Original languageEnglish
Pages (from-to)307-311
Number of pages5
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 12 Nov 1992

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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