Before revision: For any constants d\ge 1, \epsilon >0, t>1, and any n-point set P\subsetR^d, we show that there is a geometric graph G=(P,E) having O(n\log ^4 n\log\log n) edges with the following property:
After revision: For any constants d\ge 1, \epsilon >0, t>1, and any n-point set P\subsetR^d, we show that there is a geometric graph G=(P,E) having O(n\log ^2 n\log\log n) edges with the following property: