Abstract
Fos S ⊆ R, let G(Sd) denote the graph, obtained from all the points of the real d-space Rd having their coordinates in S, by connecting every two points which are at distance one. If S = Q (the rationals), or Q[√k], or Q[a] where a is a real algebraic number, then G(Sd) is shown to be connected for all large values of d. Similar results are obtained in the case of S = Q[n k], where the distance is computed in the lp-norm, p an integer, p ≥ 3 and n∥p (or n = 2).
Original language | English |
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Pages (from-to) | 143-150 |
Number of pages | 8 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 49 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1990 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics