Even Cycles in Graphs with Many Odd Cycles

  title={Even Cycles in Graphs with Many Odd Cycles},
  author={Ralph J. Faudree and Evelyne Flandrin and Michael S. Jacobson and Jen{\"o} Lehel and Richard H. Schelp},
  journal={Graphs and Combinatorics},
It will be shown that if G is a graph of order n which contains a triangle, a cycle of length n or nÿ 1 and at least cn odd cycles of di ̈erent lengths for some positive constant c, then there exists some positive constant k ˆ k…c† such that G contains at least kn even cycles of di ̈erent lengths. Other results on the number of even cycle lengths which appear in graphs with many di ̈erent odd length cycles will be given. 

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