Abstract: In the study on path decomposition of the hypercube [Qn], it is proved that a [{Pn+1}]-decomposition exists. This paper gives a sufficient and necessary condition of [{P4}]-decomposition and a sufficient condition of [{P3,P4}]-decomposition for hypercube respectively. By properties of hypercube and path decomposition conclusions, its path decomposition algorithm is proposed.

Key words: hypercube [Qn], path decomposition, 1-factor

摘要： 在超方体[Qn]的路分解的研究中，证明了[Qn]存在[{Pn+1}]-分解的定理；分别给出了[Qn]存在[{P4}]-分解的充分必要条件和存在[{P3,P4}]-分解的充分条件；结合超方体的性质和路分解结论，设计出超方体的路分解算法程序。

关键词: 超方体[Qn], 路分解, 1-因子