AI 中文总结
本文证明了完全多部图中定向哈密顿路径与回路的计数公式，采用折叠技术关联普通路径图与合法着色路径图。
AI 中文摘要
我们证明了任意完全多部图中定向哈密顿路径和定向哈密顿回路数量的计数公式。该方法基于一种折叠技术，将带有彩色顶点的普通路径图与合法着色的路径图联系起来。
英文摘要
We prove counting formulae for the number of directed Hamiltonian paths and directed Hamiltonian cycles in any complete multipartite graph. The method is based on a collapsing technique relating general path graphs with coloured vertices to legally coloured path graphs.
