Degree Conditions for Claw-Free Graphs to Have Spanning Trees with at Most Five Branch Vertices and Leaves in Total

Abstract

A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree at least three. In this paper, we show a degree condition for a claw-free graph to have spanning trees with at most five branch vertices and leaves in total. Moreover, the degree sum condition is best possible.