Geodesic
Spanning trees with a bounded number of branch vertices in a $K_{1,4}$-free graph
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1195-1202

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In 2008, it was conjectured that, for any positive integer k, a connected n-vertex graph G must contain a spanning tree with at most k branch vertices if σ_k+3(G)≥ n-k. In this paper, we resolve this conjecture in the affirmative for the graphs K_ 1,4-free.
Keywords: spanning tree, branch vertices, $K_{1,4}$-free 
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     title = {Spanning trees with a bounded number of branch vertices in a $K_{1,4}$-free graph},
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Hanh, Dang Dinh. Spanning trees with a bounded number of branch vertices in a $K_{1,4}$-free graph. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1195-1202. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a16/