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Let $T$ be a tree, a vertex of degree one is called a leaf. The set of leavesof $T$ is denoted by $Leaf(T)$. The subtree $T-Leaf(T)$ of $T$ is called thestem of $T$ and denoted by $Stem(T).$ In this note, we give a sharp sufficientcondition to show that a $K_{1,t}-$free graph has a spanning tree whose stemhas a few leaves. By applying the main result, we give improvements of previousrelated results.

A note on spanning trees of connected $K_{1,t}$-free graphs whose stems have a few leaves