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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.

The Rupture Degree of Graphs with &lt;i&gt;k&lt;/i&gt;-Tree

The Rupture Degree of Graphs with <i>k</i>-Tree