完全二部图的Kp,p-分解大集的存在谱

The Existence Spectrum of Large Sets of Kp,p-decomposition of Complete Bipartite Graphs

令H,G是两个简单图,G是H的一个子图.H的G-分解,记为（λH,G）-GD,是指将图λH的所有边分拆为若干个与G同构的子图（称为G-区组）.H的G-分解的大集,记为（λH,G）-LGD,是指图H的所有与G同构的子图的一个分拆Β1,Β2,…,Βm,使得每个Bj（1≤j≤m）为一个（λH,G）-GD （称为小集）.本文中,我们对完全二部图的K（p,p）-分解的大集进行了研究,利用Kv的λ重Kκ-因子大集的存在性结果,采用直接构造的方法,得到了大集（λK（m,n）,K（p,p））-LGD的存在谱,其中p为任意素数.

Let H, G be two simple graphs, where G is a subgraph of H. A G-decomposition of H, denoted by （λH, G）-GD, is a partition of all the edges of λH into subgraphs （called G-blocks）, each of which is isomorphic to G. A large set of （λH, G）-GD, denoted by （λH, G）- LGD, is a partition of all subgraphs of H that are isomorphic to G into B1, B2,..., Bm, such that each Bj （1 ≤ j ≤ m） is a （λN, G）-GD （called small set）. In this paper, we investigate the large sets of Kp,p-decomposition of complete bipartite graphs. Combining the existence result of large sets of λ-fold Kk-factor of Kv, we obtain the existence spectrum of （λKm,n, Kp,p）-LGD by using direct constructions, where p is a prime.