Finding and counting given length cycles

@article{Alon1997FindingAC,
  title={Finding and counting given length cycles},
  author={Noga Alon and Raphael Yuster and Uri Zwick},
  journal={Algorithmica},
  year={1997},
  volume={17},
  pages={209-223}
}
We present an assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs. Most of the bounds obtained depend solely on the number of edges in the graph in question, and not on the number of vertices. The bounds obtained improve upon various previously known results. 

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