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Graphs and Combinatorics

, Volume 16, Issue 4, pp 399–410 | Cite as

Even Cycles in Graphs with Many Odd Cycles

  • Ralph J. Faudree
  • Evelyne Flandrin
  • Michael S. Jacobson
  • Jenő Lehel
  • Richard H. Schelp
  • 55 Downloads

Abstract.

It will be shown that if G is a graph of order n which contains a triangle, a cycle of length n or n−1 and at least cn odd cycles of different lengths for some positive constant c, then there exists some positive constant k=k(c) such that G contains at least kn1/6 even cycles of different lengths. Other results on the number of even cycle lengths which appear in graphs with many different odd length cycles will be given.

Keywords

Cycle Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 2000

Authors and Affiliations

  • Ralph J. Faudree
    • 1
  • Evelyne Flandrin
    • 2
  • Michael S. Jacobson
    • 3
  • Jenő Lehel
    • 3
  • Richard H. Schelp
    • 4
  1. 1.Department of Mathematics Sciences, University of Memphis, Memphis, TN 38152, USAUS
  2. 2.L.R.I., URA 410 CNRS, Université Paris-Sud, Bât. 490, 91405 Orsay cedex FranceFR
  3. 3.Department of Mathematics, University of Louisville, Louisville, KY 40292, USAUS
  4. 4.Department of Mathematics Sciences, University of Memphis, Memphis, TN 38152, USAUS

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