Abstract
Fort fixed,n+t pointsA 1,A 2,...,A n andB 1,B 2,...,B t are constructed in the plane withO(√n) distinct distancesd(A i B j ) As a by-product we show that the graph of thek largest distances can contain a complete subgraphK t, n withn=Θ(k 2), which settles a problem of Erdős, Lovász and Vesztergombi.
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References
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P. Erdős, L. Lovász, K. Vesztergombi: On graphs of large distancesDiscrete and Computational Geometry,4 (1989), 541–549.
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Research partially supported by the Hungarian National Science Fund (OTKA) # 2117.