Geodesic
Spanning Trees whose Stems have a Bounded Number of Branch Vertices
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 773-778

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Let T be a tree, a vertex of degree one and a vertex of degree at least three is called a leaf and a branch vertex, respectively. The set of leaves of T is denoted by Leaf(T). The subtree T − Leaf(T) of T is called the stem of T and denoted by Stem(T). In this paper, we give two sufficient conditions for a connected graph to have a spanning tree whose stem has a bounded number of branch vertices, and these conditions are best possible.
Keywords: spanning tree, stem, branch vertex 
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Yan, Zheng. Spanning Trees whose Stems have a Bounded Number of Branch Vertices. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 773-778. http://geodesic.mathdoc.fr/item/DMGT_2016_36_3_a18/