Even Cycles in Graphs with Many Odd Cycles |
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| Authors: | Ralph J Faudree Evelyne Flandrin Michael S Jacobson Jen? Lehel Richard H Schelp |
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| Institution: | (1) Department of Mathematics Sciences, University of Memphis, Memphis, TN 38152, USA, US;(2) L.R.I., URA 410 CNRS, Université Paris-Sud, Bat. 490, 91405 Orsay cedex France, FR;(3) Department of Mathematics, University of Louisville, Louisville, KY 40292, USA, US;(4) Department of Mathematics Sciences, University of Memphis, Memphis, TN 38152, USA, US |
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| 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 kn
1/6 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.
Received: October 15, 1997 |
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