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Nesting of cycle systems of odd length

✍ Scribed by C.C. Lindner; C.A. Rodger; D.R. Stinson


Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
780 KB
Volume
77
Category
Article
ISSN
0012-365X

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✦ Synopsis


m edges {x1, x2}, {x2, x3}, . . . , {x,,,_~, x,}, {x,, xl} such that the vertices x1


πŸ“œ SIMILAR VOLUMES


Small embeddings for partial cycle syste
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We prove that if m is odd then a partial m-cycle system on n vertices can be embedded in an m-cycle system on at most m((m -2)n(n -1) + 2n + 1) vertices and that a partial weak Steiner m-cycle system on n vertices can be embedded in an m-cycle system on m(2n + 1) vertices.

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Three obvious necessary conditions for the existence of a k-cycle system of order n are that if n > 1 then n 1 k, n is odd, and 2 k divides n(n -1). We show that if these necessary conditions are sufficient for all n satisfying k I n < 3k then they are sufficient for all n. In particular, there exis

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## Abstract In this article, we introduce a new technique for obtaining cycle decompositions of complete equipartite graphs from cycle decompositions of related multigraphs. We use this technique to prove that if __n__, __m__ and Ξ» are positive integers with __n__ β‰₯ 3, Ξ»β‰₯ 3 and __n__ and Ξ» both odd

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