Graphs and Combinatorics

, Volume 12, Issue 3, pp 295–303 | Cite as

On the connectivity of unit distance graphs

  • Michael Reid


For a number field K ⊆ ℝ, consider the graph G(K d ), whose vertices are elements of K d , with an edge between any two points at (Euclidean) distance 1. We show that G(K 2) is not connected whileG(K d ) is connected ford ≥ 5. We also give necessary and sufficient conditions for the connectedness of G(K 3) and G(K 4).


Chromatic Number Number Field Quadratic Extension Additive Coloring Real Closed Field 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Michael Reid
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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