The number of vertices of degree k in a minimally k-edge-connected digraph

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	The number of vertices of degree k in a minimally k-edge-connected digraph
	Yuan, XD; Kang, LY; Cai, MC
	2000-02-01
发表期刊	JOURNAL OF GRAPH THEORY
ISSN	0364-9024
卷号	33 期号:2 页码:94-108
摘要	Let k be a positive integer, and D = (V(D), E(D)) be a minimally k-edge-connected simple digraph. We denote the outdegree and indegree of x is an element of V(D) by delta(D)(x) and rho(D)(x), respectively. Let uf(D) denote the number of vertices x in D with delta(D) (x) = k, rho(D)(x) > k; u(+/-)(D) the number of vertices x with delta(D) (x) = rho(D)(x) = k;u(-)(D) the number of vertices x with delta(D)(x) > k, rho(D)(x) = k. W. Mader asked the following question in [Mader, in Paul Erdos is Eighty, Keszthely, Budapest, 1996]. for each k greater than or equal to 4, is there a c(k) > 0 such that u(+)(D) + 2u(+/-)(D) + u(-)(D) greater than or equal to c(k)\D\ holds? where \D\ denotes the number of the vertices of D: In this article, we give a partial result for the question. It is proved that, for \D\ greater than or equal to 2k - 2, [GRAPHICS] (C) 2000 John Wiley & Sons, Inc.
关键词	k-edge-connected degree tree representation
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000084904900004
出版者	JOHN WILEY & SONS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15458
专题	中国科学院数学与系统科学研究院
通讯作者	Yuan, XD
作者单位	Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Yuan, XD,Kang, LY,Cai, MC. The number of vertices of degree k in a minimally k-edge-connected digraph[J]. JOURNAL OF GRAPH THEORY,2000,33(2):94-108.
APA	Yuan, XD,Kang, LY,&Cai, MC.(2000).The number of vertices of degree k in a minimally k-edge-connected digraph.JOURNAL OF GRAPH THEORY,33(2),94-108.
MLA	Yuan, XD,et al."The number of vertices of degree k in a minimally k-edge-connected digraph".JOURNAL OF GRAPH THEORY 33.2(2000):94-108.