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

摘要: 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 ,C5-强制分解存在的必要条件也是充分的

Abstract: 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.