On a Quasi-Ramsey problem

@article{Erds1983OnAQ,
  title={On a Quasi-Ramsey problem},
  author={Paul Erd{\"o}s and J{\'a}nos Pach},
  journal={Journal of Graph Theory},
  year={1983},
  volume={7},
  pages={137-147}
}
It is proved that if a graph G has at least cn log n vertices, then either G or its complement G contains a subgraph H with at least n vertices and minimum degree at least I V(H) I /2. This result is not far from being best possible, as is shown by a rather unusual random construction . Some related questions are also discussed . 

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Rothschild, and J. Spencer, Ramsey Theory. Wiley, New York • 1980
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