Geodesic
On a Spanning $k$-Tree in which Specified Vertices Have Degree Less Than $k$
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 191-196

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A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σ_k(G) ≥ |V (G)|+s−1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree less than k. The degree condition is sharp.
Keywords: spanning tree, degree bounded tree, degree sum condition 
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     author = {Matsumura, Hajime},
     title = {On a {Spanning} $k${-Tree} in which {Specified} {Vertices} {Have} {Degree} {Less} {Than} $k$},
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Matsumura, Hajime. On a Spanning $k$-Tree in which Specified Vertices Have Degree Less Than $k$. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 191-196. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a14/