完全等部多重图的变长圈分解：混合分离法
Decomposing complete equipartite multigraphs into cycles of variable lengths: the amalgamation-detachment approach
摘要：
利用混合分离技术，证明了完全等部多重图$λK_{n\times m}$可分解为长度为$c_1m,\dots,c_km$（如果度是奇数，则加1-因子）的圈，只要$λm K_n$存在分解为长度为$c_1, \dots,c_k$（如果度是奇数，则加1-因子）的圈.此外，我们还给出了完全等部多重图$λK_{n\times m}$存在其他一些相关的圈分解的充分条件。
英文摘要：
Using the technique of amalgamation-detachment, we show that the complete equipartite multigraph $λK_{n\times m}$ can be decomposed into cycles of lengths $c_1m,\dots,c_km$ (plus a 1-factor if the degree is odd) whenever there exists a decomposition of $λm K_n$ into cycles of lengths $c_1, \dots,c_k$ (plus a 1-factor if the degree is odd). In addition, we give sufficient conditions for the existence of some other, related cycle decompositions of the complete equipartite multigraph $λK_{n\times m}$.
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