Cycle Decomposition of Complete Graphs

研究的主要问题是完全图的循环分解。目的是找到n的值，使有n个顶点的完全图分解成固定奇数长度的循环。与循环分解相关的其他问题将被研究，例如循环系统的可解性和嵌套性。循环分解构成了邻域设计的一个特例，邻域设计在统计实验设计中有许多应用，特别是在平衡不完全块设计中。

The main problem to be studied concerns cycle decompositions of complete graphs. The aim is to find the values of n for which complete graphs with n vertices have a decomposition into cycles of fixed odd length. Other problems related to cycle decompositons will be studied, such as the resolvability and nesting of cycle systems. Cycle decompositions constitute a special case of neighborhood designs which have found numerous applications in the design of statistical experiments, in particular of balanced incomplete block designs.