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应用数学学报  2013, Vol. 36 Issue (6): 1072-1079    DOI:
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完全二部图的K3,3-分解的大集
张艳芳
河北经贸大学数学与统计学学院, 石家庄 050061
Large Sets of K3,3-decomposition of Complete Bipartite Graphs
ZHANG Yanfang
College of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061
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摘要 HG是两个简单图,GH的一个子图. HG-分解,记为(λHG)-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). HG-分解的大集,记为(λHG)-LGD,是指图H的所有与G同构的子图的一个分拆B1B2,…,Bm,使得每个Bj (1≤jm)为一个(λHG)-GD (称为小集). 若H的一个生成子图G可以分拆为一些与F同构的子图,且每个顶点出现在与F同构的子图中个数均为λ,则称GH的一个λF-因子,记为Sλ(1,FH). 图HλF-因子大集,记为LSλ(1,FH),是图H中所有与F同构的子图的一个分拆{Bi}i,使得每个Bi均为一个Sλ(1,FH). 本文中,我们研究了完全二部图的K3,3-分解的大集问题,利用大集LSλ(1,KkKv)的存在性结果,采用直接构造的方法,得到了大集(λKmnK3,3)-LGD的存在谱.
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张艳芳
关键词大集   K3,3-分解   完全二部图     
Abstract: 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 isomorphic to G of H into B1, B2, …,Bm, such that each Bj (1≤jm) is a (λH,G)-GD (called small set). Let G be a spanning subgraph of H, if G can be partitioned into some subgraphs isomorphic to F, and the number of each vertex of G appears in subgraphs isomorphic to F is exactly λ, then G is called a λ-fold F-factor of H, denoted by Sλ(1,F,H). A large set of λ-fold F-factors of H, denoted by LSλ(1,F,H), is a partition {Bi}i of all subgraphs of H isomorphic to F, such that each {Bi} forms a λ-fold F-factor of H. In this paper, we investigate the large sets of K3,3-decomposition of complete bipartite graphs. Combining the existence result of LSλ(1,Kk,Kv), we obtain the existence spectrum of (λKm,n,K3,3)-LGD by using direct construtions.
Key wordslarge set   K3,3-decomposition   complete bipartite graph   
收稿日期: 2013-05-14;
基金资助:河北省自然科学基金(A2010001481,A2012207001)资助项目.
引用本文:   
张艳芳. 完全二部图的K3,3-分解的大集[J]. 应用数学学报, 2013, 36(6): 1072-1079.
ZHANG Yanfang. Large Sets of K3,3-decomposition of Complete Bipartite Graphs[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(6): 1072-1079.
 
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