\input zb-basic
\input zb-ioport
\iteman{io-port 06010663}
\itemau{Hao, Guohui; Kang, Qingde}
\itemti{Large sets of $\lambda $-fold $P_3$-factors in $K_{V,V}$.}
\itemso{Ars Comb. 96, 321-329 (2010).}
\itemab
Summary: Let $G$ be a finite graph and $H$ be an subgraph of $G$. If $V(H)=V(G)$ then the subgraph $H$ is called a spanning subgraph of $G$. A spanning subgraph $H$ of $G$ is called an $F$-factor if each component of $H$ is isomorphic to $F$. Further, if there exists a subgraph of $G$ whose vertex set is $\lambda V(G)$ and can be partitioned into $F$-factors then it is called a $\lambda $-fold $F$-factor of $G$, denoted by $S_\lambda (1,F,G)$. A large set of $\lambda $-fold $F$-factors in $G$ is a partition $\{\Cal B_i\}_i$ of all subgraphs of $G$ isomorphic to $F$, such that each $(X,\Cal B_i)$ forms a $\lambda $-fold $F$-factor of $G$. In this paper we investigate the large set of $\lambda $-fold $P_3$-factors in $K_{v,v}$ and obtain its existence spectrum.
\itemrv{~}
\itemcc{}
\itemut{large set; Hamilton cycle; $P_3$-factor; $LS_\lambda (1,P_3,K_{v,v})$}
\itemli{}
\end