关于正则图的路分解

Path Decomposition of Regular Graphs

在3 正则图的{P3,P4}分解的基础上,结合偶次图的圈分解,证明了任意的4 正则图存在{P4,P5}分解,任意的5 正则图存在{P5,P6}-的分解。同时还提出了k 正则图路分解的猜想。

This paper discusses the path decomposition of regular graphs based on the path decomposition of 3-regular graph and cycle decomposition of even-degree graph and proves that there exits a { P4, P5 } -decomposition for a 4-regular graph and { P5, P6 } -decomposition for any 5-regular graph.