关于多部图K_n(t)的{D,C_4}——强制分解

On Mandatory Decompositions of Complete Mulipartite Graph into C_4 and D

设n,t为正整数,以Kn(t)表示基于顶点集X=Xi上的完全n部图,其中｜X1｜=｜X2｜=……=｜Xn｜=t。文章研究了完全多部图Kn(t)的狖D,C4狚———分解,使得分解中至少有一个D和一个C4,称这样的分解为Kn(t)的狖D,C4狚———强制分解。文章给出了Kn(t)的狖D,C4狚———强制分解存在的必要且充分条件。

let n and t be positive integers. We use notation Kn(t) to denote the complete n-partite multi-graph based on vertex set X= ,in which |X1|=|X2|=…=|Xn|=t. The paper gives the necessary and sufficient conditions of the existence of mandatory decompositions of complete mulipartite graph into C4 and D.