𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The complete spectrum of 6-cycle systems of l(kn)

✍ Scribed by B. A. Cox


Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
533 KB
Volume
3
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ 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).


πŸ“œ SIMILAR VOLUMES


Cyclic even cycle systems of the complet
✍ Shung-Liang Wu πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 164 KB πŸ‘ 1 views

## 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__‐cycle system of __K__~__n__~, which almost resolves the existence problem for cyclic __m__‐cycle systems of __K__~__n__~ with __m__ even. Β© 201

Cyclic Hamiltonian cycle systems of the
✍ Marco Buratti; Alberto Del Fra πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 251 KB

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

Cycle systems of the line graph of the c
✍ Cox, B.A.; Rodger, C.A. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 562 KB

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.

Cyclic k-cycle systems of order 2kn + k:
✍ Andrea Vietri πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 144 KB

## Abstract We exhibit cyclic (__K~v~__, __C~k~__)‐designs with __v__ > __k__, __v__ ≑ __k__ (mod 2__k__), for __k__ an odd prime power but not a prime, and for __k__ = 15. Such values were the only ones not to be analyzed yet, under the hypothesis __v__ ≑ __k__ (mod 2__k__). Our construction avail

On the Spectrum, Complete Trajectories,
✍ V.Q. Phong πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 594 KB

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)\}