Spanning trees with at most 2 branch vertices in claw - free graphs

Abstract

In this article, we will prove that if $G$ is a connected claw-free graph and either ${\sigma }_6(G)\ge |G|-5$ or ${\sigma }_7(G)\ge |G|-2$, here ${\sigma }_k(G)$ is the minimmum degree sum of $k$ independent vertices in $G$, then $G$ has a spanning tree with at most two branch vertices.