关于完全多部图K_n(t)的{C_3,C_4,C_5}-强制分解

Mandatory decomposition of complete multipartite graph into cycles of lengths 3,4 and 5

Kn( t)的 {Ci,Cj,Ck}-强制分解是指将 Kn( t)分解为长为 i或 j或 k的圈 ,并且分解中至少有一个长为 i,j和 k的圈 .本文证明了多部图 Kn( t)的 {C3,C4 。

A {C_i,C_j,C_k}-mandatory decomposition of K_n(t) is a decomposition of K_n(t) into cycles of lengths i,j,or k such that there are at least one cycle of lengths i,j,and k in the decomposition. In this paper, it is proved that the necessary conditions for the existence of a {C_3,C_4,C_5}-mandatory decomposition of K_n(t) are also sufficient.