完全r部图K_r(t)的{C_3,C_(2k)}-强制分解

Mandatory Decompositions of Complete Multipartite Graphs into Cycles of Lengths 3 or 2k

本文研究完全多部图的强制圈分解的存在性问题,得到了完全r部图Kr(t)的3圈和2k圈{C2,C2k}-强制分解存在时t与r的4种可能关系,特别地,给出了k=2,3时t与r满足这些关系之一为强制分解存在的充分条件。

The existence problem for a {C3,C2k}-mandatory decomposition of Kr（t） is discussed. Four relations between r and t are given which is a necessary condition for the problem. When k is 2 or 3, the necessary condition is also sufficient.