A Density Version of a Geometric Ramsey Theorem

  title={A Density Version of a Geometric Ramsey Theorem},
  author={Tom C. Brown and Joe Buhler},
  journal={J. Comb. Theory, Ser. A},
Let V be an n-dimensional affine space over the field with pd elements, p 6= 2. Then for every ε > 0 there is an n(ε) such that if n = dim(V ) n(ε) then any subset of V with more than εjV j elements must contain 3 collinear points (i.e., 3 points lying in a one-dimensional affine subspace). 

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