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六点七边图的λ-填充与λ-覆盖(英文)
λ-packings andλ-coverings by Graphs With Six Vertices and Seven Edges

杜艳可;康庆德;
DU Yanke~

军械工程学院基础部;河北师范大学数学研究所;
(1,*) KANG Qingde~2 1.Dept.of Basic Courses,Ordnance Engineering College,Shijiazhuang,Hebei,050003,P.R.China; 2.Institute of Math.,Hebei Normal University,Shijiazhuang,Hebei,050016,P.R.Chin

收稿日期: 2009-02-25
出版日期: 2009-02-25

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摘要 λK_v为λ重v点完全图,G为有限简单图,λK_v的一个G-设计(G-填充设计,G-覆盖设计),记为(v,G,λ)-GD((v,G,λ)-PD,(v,G,λ)-CD),是指一个序偶(X,B),其中X为K_v的顶点集,B为K_v中同构于G的子图的集合,称为区组集,使得K_v中每条边恰好(至多,至少)出现在B的λ个区组中.一个填充(覆盖)设计称为最大(最小)的,如果没有其它的填充(覆盖)设计有更多(更少)的区组.本文中,我们构作了三个六点七边图的最大填充与最小覆盖.
关键词 G-设计G-填充设计G-覆盖设计    
Abstract:LetλK_v,be the complete multigraph with v vertices and G a finite simple graph. A G-design(G-packing design,G-covering design)ofλK_v,denoted by(v,G,λ)-GD((v,G,λ)- PD,(v,G,λ)-CD),is a pair(X,B)where X is the vertex set of K_v and B is a collection of subgraphs of K_v,called blocks,such that each block is isomorphic to G and any two distinct vertices in K_v are joined in exactly(at most,at least)λblocks of B.A packing(covering)design is said to be maximum(minimum)if no other such packing(covering)design has more(fewer) blocks.In this paper,a maximum(v,G,λ)-PD and a minimum(v,G,λ)-CD are constructed for 3 graphs of 6 vertices and 7 edges.
Key wordsG-packing design    G-covering design
[1] 张艳芳, 王国强. λ重完全图λKv的4类图最优填充和最优覆盖[J]. 数学进展, 2019, 48(1): 35-44.
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