m-dominating k-trees of graphs | |
Kano, Mikio1; Ozeki, Kenta2,3; Tsugaki, Masao4; Yan, Guiying5![]() | |
刊名 | DISCRETE MATHEMATICS
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2016-02-06 | |
卷号 | 339期号:2页码:729-736 |
关键词 | k-tree Dominating tree n-connected graph |
ISSN号 | 0012-365X |
DOI | 10.1016/j.disc.2015.10.013 |
英文摘要 | Let k (>=) 2, l >= 2, m >= 0 and n >= 1 be integers, and let G be a connected graph. If there exists a subgraph H of G such that for every vertex v of G, the distance between v and H is at most m, then we say that H m-dominates G. A tree whose maximum degree is at most k is called a k-tree. Define alpha(1)(G) = max{vertical bar S vertical bar : S subset of V(G), d(G)(x,y) >= l for all distinct x, y is an element of SI, where d(G)(x, y) denotes the distance between x and y in G. We prove the following theorem and show that the condition is sharp. If an n-connected graph G satisfies alpha(2(m+1)) (G) <= (k - 1)n+1, then G has a k-tree that m-dominates G. This theorem is a generalization of both a theorem of Neumann-Lara and Rivera-Campo on a spanning k-tree in an n-connected graph and a theorem of Broersma on an m-dominating path in an n-connected graph. (c) 2015 Elsevier B.V. All rights reserved. |
资助项目 | JSPS KAKENHI Grant[25400187] ; JSPS KAKENHI Grant[25871053] ; The Sumitomo Foundation ; Chinese Academy of Science[2012Y1JA0004] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | ELSEVIER SCIENCE BV |
WOS记录号 | WOS:000367630800038 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/21710] ![]() |
专题 | 应用数学研究所 |
通讯作者 | Kano, Mikio |
作者单位 | 1.Ibaraki Univ, Hitachi, Ibaraki, Japan 2.Res Org Informat & Syst, Natl Inst Informat, Chiyoda Ku, Tokyo 1018430, Japan 3.JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan 4.Tokyo Univ Sci, Shinjuku Ku, Tokyo 162, Japan 5.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
推荐引用方式 GB/T 7714 | Kano, Mikio,Ozeki, Kenta,Tsugaki, Masao,et al. m-dominating k-trees of graphs[J]. DISCRETE MATHEMATICS,2016,339(2):729-736. |
APA | Kano, Mikio,Ozeki, Kenta,Tsugaki, Masao,&Yan, Guiying.(2016).m-dominating k-trees of graphs.DISCRETE MATHEMATICS,339(2),729-736. |
MLA | Kano, Mikio,et al."m-dominating k-trees of graphs".DISCRETE MATHEMATICS 339.2(2016):729-736. |
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