On the panconnectivity of graphs with large degrees and neighborhood unions

	On the panconnectivity of graphs with large degrees and neighborhood unions
	Wei, B; Zhu, Y
刊名	GRAPHS AND COMBINATORICS
	1998
卷号	14 期号:3 页码:263-274
ISSN号	0911-0119
英文摘要	Let G be a 2-connected graph on n vertices and delta be the minimum degree of G( V, E). Set NC = min{/N(u) boolean OR N(v)/ : u, v epsilon V, uv is not an element of E}. In this paper, we show that if for any independent set {u, v, w} of G, we have min{/N(u) boolean OR N(v)/ + d(w), /N(u) boolean OR N(w)/ + d(v), /N(v) boolean OR N(w)/ + d(u)} greater than or equal to n + 1, then for any integer 7 less than or equal to i less than or equal to n and any vertices x,y such that {x, y} is not a cut vertex set of G, there exists a path connecting u, v with i vertices in G. In particular, if G is 3-connected, then G is [7,n]-panconnected. Using this result, we can prove that if NC + delta greater than or equal to n + 1, then G is vertex pancyclic. This was conjectured by Faudree, Gould, Jacobson and Lesniak.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER VERLAG
WOS记录号	WOS:000076772900004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/13502]
专题	中国科学院数学与系统科学研究院
作者单位	Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wei, B,Zhu, Y. On the panconnectivity of graphs with large degrees and neighborhood unions[J]. GRAPHS AND COMBINATORICS,1998,14(3):263-274.
APA	Wei, B,&Zhu, Y.(1998).On the panconnectivity of graphs with large degrees and neighborhood unions.GRAPHS AND COMBINATORICS,14(3),263-274.
MLA	Wei, B,et al."On the panconnectivity of graphs with large degrees and neighborhood unions".GRAPHS AND COMBINATORICS 14.3(1998):263-274.