Cycle Decomposition of Complete Graphs

完全图的循环分解

• 批准号: 8805475
• 负责人: Christopher Rodger
• 金额: $ 3.68万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-10-15 至 1991-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805475&HistoricalAwards=false
• 关键词: Cycle; Decomposition; Complete; Graphs

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.

要研究的主要问题涉及完全图的循环分解。 目的是找到 n 的值，使具有 n 个顶点的完整图分解为固定奇数长度的循环。 将研究与循环分解相关的其他问题，例如循环系统的可解性和嵌套。 循环分解构成了邻域设计的一个特例，它在统计实验设计中得到了广泛的应用，特别是平衡不完全区组设计。