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).
|Number of pages||8|
|Journal||Journal of Combinatorial Theory. Series B|
|State||Published - Aug 1990|
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics