摘要: G-设计是可分组设计(
GD)的推广,同时又是烛台型设计(CQS)的特例,它在四元系设计中起到重要作用。文章应用Stern和Lenz关于图因子分解的结论,通过直接构造法,得到具有三个组的G-设计
![](https://image.hanspub.org/IMAGE/Edit_c3b872ab-e32f-444d-9d2d-bc353703534a.jpg)
存在的充分必要条件:
![](https://image.hanspub.org/IMAGE/Edit_467b227c-0a41-45bb-b06d-db9eff9f7fb3.jpg)
。
Abstract:
As a special example of the candelabra systems (CQS),
G-design is the extension of group divisible designs (
GD), which plays an important role in quadruple systems’ construction. With application of Stern and Lenz’s result on one-factorization of graphs, by direct construction, it is given that the sufficient and necessary condition for the existence of the G-design with three groups
![](https://image.hanspub.org/IMAGE/Edit_dc1405a5-4c0e-45d0-9e87-9e541af95308.jpg)
is that
![](https://image.hanspub.org/IMAGE/Edit_2445dad7-d623-4f9e-a7d1-77f78404a817.jpg)
.