λK_(m,n)的P_k-分解  

P_k-Decomposition of λK_(m,n)

作　　者：施静[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《南通职业大学学报》2007年第1期98-100,共3页Journal of Nantong Vocational University

基　　金：国家自然科学基金资助项目(10571133)

摘　　要：λKm,n的Pk-分解就是一个(X,B),其中X是Km,n的顶点集,B是Km,n的子图族,每个子图(称为区组)均同构于Pk,且Km,n中任一边都恰好出现在B的!个区组中。Ushio在其综述文献中提出了!Km,n的Pk-分解存在性问题的一个猜想。文章证明了该猜想当k=4,5时成立。A Pk-decomposition of lKm,n is a pair （X, B） where X is the vertex set of Km,n, and B is a collection of subgraphs of Km,n, called blocks, such that each block is isomorphic to Pk and any two distinct vertices in Km,n are joined in exactly l blocks of B. Ushio proposed a conjecture on the existence of a Pk-decomposition of lKm,n. This paper proves that Ushio conjecture is true when k=4, 5.

关 键 词：完全二部图 Pk-分解 Ushio猜想 

分 类 号：O157[理学—数学]