完全二部图的λ重K_(p,p-)因子大集的存在谱

The Existence Spectrum of Large Set of λ-fold K_(p,p)-factor of Complete Bipartite Graph

若G的一个生成子图H可以分拆为一些与F同构的子图(称为F-区组),且G的每个顶点恰出现在λ个F-区组中,则称H为G的一个λ重F-因子,记为S_λ(1,F,G).图G的λ重F-因子大集,记为LS_λ(1,F,G),是图G中所有与F同构的子图的一个分拆{B_i}i,使得每个B_i均为一个S_λ(1,F,G).本文中,我们研究了完全二部图K_(m,n)的λ重K_(p,p-)因子大集(即LS_λ(1,K_(p,p),K_(m,n)))的存在性,并且得到了该大集的存在谱,其中p是任意素数.

Let H be a spanning subgraph of G, if H can be partitioned into some subgraphs isomorphic to F （called F-blocks）, and each vertex of G appears in exactly λ blocks, then H is called a λ-fold F-factor of G, denoted by Sλ（1, F, G）. A large set of λ-fold F-factor of G, denoted by LSλ（1, F, G）, is a partition {Bi}i of all subgraphs of G isomorphic to F, such that each Bi is a λ-fold F-factor of G. In this paper, we investigate the large set of λ-fold Kp,p-factor of Km,n （i.e. LSλ（1, Kp,p, Km,n）） and obtain its existence spectrum, where p is a prime.