关于多部图K_n(t)的｛K_4-e,S_3｝—强制分解

Mandatory Decompositions of Complete Multipartite Graph into K_4-e and S_3

设n,t为正整数,以K_n(t)表示基于顶点集X=■X_i上的完全n部图。文章证明了(Kn(t),｛K4-e,S3｝)—强制分解存在当且仅当n≥3且(n,t)≠(3,2)。

Let n and t be positive integers. We use notation K,（t） to denote the complete n-partite multigraph based on vertex set X= Ui-1^nXi. In this paper, we showed that a mandatory decompositions of complete multipartite graph into K4-e and S3 exist if and only ifn≥3 and （n,t）≠（3,2）.