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A small embedding for partial even-cycle systems

✍ Scribed by Peter Horak; C. C. Lindner

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 517 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:3<205::aid-jcd4>3.0.co;2-5

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✦ Synopsis

Let m = 2k. We show that for some 0 ≤ < 1, a partial directed m-cycle system of order n can be embedded in a directed m-cycle system of order (mn)/2 + (2m 2 + 1) (8n + 1)/4 + 4m 3 2 + 4m + 1/2. For fixed m, this is asymptotic in n to (mn)/2 and so for large n is roughly one-fourth the best known bound of 2mn + 1.

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