## Abstract In this article, it is proved that for each even integer __m__β©Ύ4 and each admissible value __n__ with __n__>2__m__, there exists a cyclic __m__βcycle system of __K__~__n__~, which almost resolves the existence problem for cyclic __m__βcycle systems of __K__~__n__~ with __m__ even. Β© 201
The complete spectrum of 6-cycle systems of l(kn)
β Scribed by B. A. Cox
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 533 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1063-8539
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β¦ Synopsis
In this article, it is shown that a decomposition of the line graph of the complete graph on n vertices into cycles of length 6 exist if and only if n p 3 (mod 4).
π SIMILAR VOLUMES
We prove that there exists a cyclic Hamiltonian k-cycle system of the complete graph if and only if k is odd but k = 15 and p with p prime and ΒΏ 1. As a consequence we have the existence of a cyclic k-cycle system of the complete graph on km vertices for any pair (k; m) of odd integers with k as abo
For all m = 0 (mod 41, for all n = 0 or 2 (mod m), and for all n = 1 (mod 2m) w e find an m-cycle decomposition of the line graph of the complete graph K,. In particular, this solves the existence problem when m is a power of two.
## Abstract We exhibit cyclic (__K~v~__, __C~k~__)βdesigns with __v__β>β__k__, __v__ββ‘β__k__ (mod 2__k__), for __k__ an odd prime power but not a prime, and for __k__β=β15. Such values were the only ones not to be analyzed yet, under the hypothesis __v__ββ‘β__k__ (mod 2__k__). Our construction avail
Let \(\{T(t)\}_{1 \geqslant 0}\) be a \(C_{0}\)-semigroup in a Banach space \(X\) with generator \(A\). We prove that if \(\{T(t)\}_{t \geqslant 0}\) is bounded and sun-reflexive, and the sun-dual semigroup is not asymptotically stable, then there exist bounded complete trajectories under \(\{T(t)\}