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

Abstract

Let T be a tree; a vertex of degree 1 is a leaf of T and a vertex of degree at least 3 is a branch vertex of T. The 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 has few leaves.