康庆德,王志芹.λKv的最大K2,3填充设计和最小K2,3覆盖设计(英文)[J].数学研究及应用,2005,25(1):1~16
λKv的最大K2,3填充设计和最小K2,3覆盖设计(英文)
Maximum K2,3-Packing Designs and Minimum K2,3- Covering Designs of λKv
投稿时间:2002-02-27  
DOI:10.3770/j.issn:1000-341X.2005.01.001
中文关键词:  G-图设计  G-填充设计  G-覆盖设计
英文关键词:G-design  G-packing design  G-covering design
基金项目:
作者单位
康庆德 河北师范大学数学研究所,河北,石家庄,050016 
王志芹 天津财经大学,天津,300222 
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中文摘要:
      对于一个有限简单图G,λKv的G-设计(G-填充,G-覆盖),记为(v,G,λ)-GD((v,G,λ)-PD,(v,G,λ)-CD),是一个(X,B),其中X是Kv的顶点集,B是Kv的子图族,每个子图(称为区组)均同构于G,且Kv中任一边都恰好(最多,至少)出现在B的λ个区组中.一个填充(覆盖)设计称为是最大(最小)的,如果没有其它的这种填充(覆盖)设计具有更多(更少)的区组.本文对于λ>1确定了(v,K2,3,λ)-GD的存在谱,并对任意λ构造了λKv的最大K2,3-填充设计和最小K2,3-覆盖设计.
英文摘要:
      Let G be a finite simple graph. A G-design (G-packing design, G-covering design)of λKv, denoted by (v, G, λ)-GD ((v, G, λ)-PD, (v, G, λ)-CD), is a pair (X, β) where X is the vertex set of Kv and β is a collection of subgraphs of Kv, called blocks, such that each block is isomorphic to G and any two distinct vertices in Kv are joined in exactly (at most, at least)λ blocks of β. A packing (covering) design is said to be maximum (minimum) if no other such packing (covering) design has more (fewer) blocks. In this paper, we determine the existence spectrum for the K2,3-designs of λKv, λ> 1, and construct the maximum packing designs and the minimum covering designs of λKv with K2,3 for any integer λ.
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