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Bondy, J.A. (1980) Longest Paths and Cycles in Graphs with High Degree. Research ReportCORR80-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo.

has been cited by the following article:

• TITLE: Closure for Spanning Trees with k-Ended Stems

  AUTHORS: Zheng Yan

  KEYWORDS: Closure, Spanning Tree, Stem, k-End Stem

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.4 No.3, June 26, 2014

  ABSTRACT: Let T be a tree. The set of leaves of Τ is denoted by Leaf(Τ). The subtree Τ—Leaf(Τ) of T is called the stem of Τ. A stem is called a k-ended stem if it has at most k-leaves in it. In this paper, we prove the following theorem. Let G be a connected graph and k≥2 be an integer. Let u and ν be a pair of nonadjacent vertices in G. Suppose that |NG(u)∪NG(v)|≥|G|-k-1. Then G has a spanning tree with k-ended stem if and only if G+uv has a spanning tree with k-ended stem. Moreover, the condition on |NG(u)∪NG(v)| is sharp.