[1]王成敏,王荣荣.2×3格子区组填充和覆盖[J].南京师范大学学报(自然科学版),2017,40(03):13.[doi:10.3969/j.issn.1001-4616.2017.03.003]
 Wang Chengmin,Wang Rongrong.2×3 Grid-Block Packings and Coverings[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(03):13.[doi:10.3969/j.issn.1001-4616.2017.03.003]
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2×3格子区组填充和覆盖()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第40卷
期数:
2017年03期
页码:
13
栏目:
·数学·
出版日期:
2017-09-30

文章信息/Info

Title:
2×3 Grid-Block Packings and Coverings
文章编号:
1001-4616(2017)03-0013-08
作者:
王成敏1王荣荣2
(1.泰州学院数理学院,江苏 泰州 225300)(2.江南大学理学院,江苏 无锡 214122)
Author(s):
Wang Chengmin1Wang Rongrong2
(1.School of Science,Taizhou University,Taizhou 225300,China)(2.School of Science,Jiangnan University,Wuxi 214122,China)
关键词:
完全图格子区组填充格子区组覆盖
Keywords:
complete graphgrid-block packinggrid-block covering
分类号:
O157.2
DOI:
10.3969/j.issn.1001-4616.2017.03.003
文献标志码:
A
摘要:
一个r×c格子区组填充(或覆盖),是一个二元组(X,A),其中XKv的顶点集,AKv的一簇与Kr×Kc同构的子图(称为格子区组),满足Kv中每一条边至多(或至少)出现在某个子图中一次. 本文研究2×3格子区组填充和覆盖的存在性. 一方面,本文解决了最大2×3格子区组填充的两个可能例外,从而完全确立了最大2×3格子区组填充的存在性; 另一方面,本文基本解决了最小2×3格子区组覆盖的存在性.
Abstract:
A r×c grid-block packing(or covering),is a pair(X,A),where X is the vertice set of Kv,A is a set of subgraphs which are isomorphism to Kr×Kc(called grid-blocks),satisfying each edge of Kv occurs at most(or at least)once in certain subgraph. In this paper,the existence of 2×3 grid-block packing and covering is considered. We first completely determined the existence of maximum 2×3 grid-block packing by removing two possible exceptions. Then we almost completely determined the existence of minimum 2×3 grid-block covering with three possible exceptions.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-01-16.
基金项目:国家自然科学基金(11471144)、江苏省自然科学基金(BK20171318).
通讯联系人:王成敏,博士,副教授,研究方向:组合设计理论及应用. E-mail:wcm@jiangnan.edu.cn
更新日期/Last Update: 2017-09-30