A Brief Proof of Spanning Trees with a Bounded Number of Leaves in a Claw-Free Graph

For a graph [see formula in PDF] and an positive integer [see formula in PDF], let [see formula in PDF] denote the minimum degree sum of [see formula in PDF] independent vertices of [see formula in PDF]. It has beenproved that if a connected claw-free graph [see formula in PDF] satisfies [see formula in PDF], then [see formula in PDF] has a spanning [see formula in PDF]-ended tree. We also know that the lower bound [see formula in PDF] is sharp. In this paper, we give a simple proof of this theorem by using another [see formula in PDF]-ended system.