Spanning trees of $K_{1,4}$-free graphs whose reducible stems have few leaves

Abstract

Let $T$ be a tree, a vertex of degree one is a \emph{leaf} of $T$ and a vertex of degree at least three is a \emph{branch vertex} of $T$. The {\it reducible stem } of $T$ is the smallest subtree that contains all branch vertices of $T$. In this paper, we give some sharp sufficient conditions for $K_{1,4}$-free graphs to have a spanning tree whose reducible stem having few leaves.