中文摘要：

令G是一个有限图,H是G的一个子图.若V（H）=V（G）,则称H为G的生成子图.图G的一个λ重F-因子,记为Sλ（F,G）,是G的一个生成子图且可分拆为若干与F同构的子图（称为F-区组）的并,使得V（G）中的每一个顶点恰出现在λ个F-区组中.一个图G的λ重F-因子大集,记为LSλ（F,G）,是G中所有与F同构的子图的一个分拆{Bi},使得每个Bi均构成一个Sλ（F,G）.当λ=1时,λ可省略不写.在[Ars Combin.,2010,96：321-329]中已经得到了LSλ（K1,2,Kv,v）的存在谱.本文证明了当v≡4（mod 12）时,存在LS（F,Kv,v,v）,这里F∈{K1,3,K2,2}.

英文摘要：

Let G be a finite graph and H be a subgraph of G. If V（H） = V（G） then the subgraph H is called a spanning subgraph of G. A A-fold F-factor of G, denoted by Sλ（F, G）, is a spanning subgraph of G, which can be partitioned into copies of F （called F-blocks）, such that each vertex of V（G） appears exactly in A F-blocks. A large set of λ-fold F-factors of G, denoted by LSλ（F, G）, is a partition {Bi} of all subgraphs of G isomorphic to F, such that eachBi forms a Sλ（F, G）. For A = 1, the index 1 is often omitted. In [Ars Cornbin., 2010, 96： 321-329], the existence spectrum for LSλ （K1,2, Kv,V） has been obtained. In this paper, it has been proved that there exists an LS（F, Kv,v,v） for v = 4 （mod 12）, where F∈ {K1,3, K2,2}.