TITLE:
The Rupture Degree of Graphs with k-Tree
AUTHORS:
Yinkui Li, Qingning Wang, Xiaoling Wang
KEYWORDS:
The Rupture Degree, k-Tree, Induced Graph
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.6 No.2,
April
22,
2016
ABSTRACT: A k-tree of a connected graph G is a spanning tree with maximum degree
at most k. The rupture degree for a
connected graph G is defined by , where and ,
respectively, denote the order of the largest component and number of
components in . In this
paper, we show that for a connected graph G,
if for any cut-set , then G has a k-tree.