Circle grids and bipartite graphs of distances


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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Research partially supported by the Hungarian National Science Fund (OTKA) # 2117.

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Elekes, G. Circle grids and bipartite graphs of distances. Combinatorica 15, 167–174 (1995).

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Mathematics Subject Classification (1991)

  • 52 A 38
  • 52 C 05