Crossing numbers of random graphs

@article{Spencer2002CrossingNO,
  title={Crossing numbers of random graphs},
  author={Joel H. Spencer and G{\'e}za T{\'o}th},
  journal={Random Struct. Algorithms},
  year={2002},
  volume={21},
  pages={347-358}
}
An order type of the points x1, x2, ..., xn in the plane (with no three colinear) is a list of orientations of all triplet xixjxk, i < j < k. Let X be the set of all order types of the points x1, ..., xn in the plane. For any graph G with vertices v1, ..., vn let lin-crξ(G) denote the number of crossings in the straight line drawing of G, where vi is placed at xi in the plane and x1, ..., xn have order type ξ ∈ X. 
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