Small subgraphs of random regular graphs

@article{Kim2007SmallSO,
  title={Small subgraphs of random regular graphs},
  author={Jeong Han Kim and Benny Sudakov and Van H. Vu},
  journal={Discrete Mathematics},
  year={2007},
  volume={307},
  pages={1961-1967}
}
The main aim of this short paper is to answer the following question. Given a fixed graph H , for which values of the degree d does a random d-regular graph on n vertices contain a copy of H with probability close to one? 

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