Abstract
AbstractAn old conjecture of Erdős states that there exists an absolute constant c and a set S of density zero such that every graph of average degree at least c contains a cycle of length in S. In this paper, we prove this conjecture by showing that every graph of average degree at least ten contains a cycle of length in a prescribed set S satisfying $|S \cap \{ 1,2,\ldots ,n\} | = O(n^{0.99})$. © 2005 Wiley Periodicals, Inc. J Graph Theory
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