Finding and counting given length cycles. Alon, N, Yuster, R., & Zwick, U. Algorithmica, 17(3):209--223, March, 1997.
Finding and counting given length cycles [link]Paper  doi  abstract   bibtex   
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.
@article{ Alon1997,
  abstract = {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.},
  author = {Alon, N and Yuster, R. and Zwick, U.},
  doi = {10.1007/BF02523189},
  file = {:Users/KunihiroWASA/Dropbox/paper/1997/Alon, Yuster, Zwick, Finding and counting given length cycles, 1997.pdf:pdf},
  issn = {0178-4617},
  journal = {Algorithmica},
  keywords = {1,a i n s,a simple cycle of,c o n t,clearly np-,cycles,d e c i,d i n g,e,e m o f,easily stated algorithmic graph,g i v e,graph algorithms,h e r a,i n t r,if the cycle length,k is part of,length k is among,n g r a,o d u c,p h g,problems,r o b l,t h e p,t i o n,the input,the most natural and,then the problem is,v,w h e t},
  month = {March},
  number = {3},
  pages = {209--223},
  title = {{Finding and counting given length cycles}},
  url = {http://link.springer.com/10.1007/BF02523189},
  volume = {17},
  year = {1997}
}

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