Elsevier

Discrete Mathematics

Volume 261, Issues 1–3, 28 January 2003, Pages 325-336
Discrete Mathematics

A partial 2k-cycle system of order n can be embedded in a 2k-cycle system of order kn+c(k),k⩾3, where c(k) is a quadratic function of k

Dedicated to Alex Rosa on the occasion of his sixty-fifth birthday
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Abstract

The bound for embedding a partial 2k-cycle system of order n,k⩾3, is dramatically improved from kn+d(k)n, where d(k) is a function of k, to kn+c(k), where c(k) is a quadratic function of k. The best known bound for 4-cycles remains 2n+10n.

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