Nesting of cycle systems of odd length
β 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
No coin nor oath required. For personal study only.
β¦ Synopsis
m edges {x1, x2}, {x2, x3}, . . . , {x,,,_~, x,}, {x,, xl} such that the vertices x1
π SIMILAR VOLUMES
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.
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
## 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
## Abstract We give an explicit solution to the existence problem for 1βrotational __k__βcycle systems of order __v__ < 3__k__ with __k__ odd and __v__ββ β2__k__β+β1. We also exhibit a 2βrotational __k__βcycle system of order 2__k__β+β1 for any odd __k__. Thus, for __k__ odd and any admissible __v__