Spanning $3$-Ended Trees in $k$-Connected Claw-Free Graphs

Abstract

Let ${\sigma }_k(G)$ denote the minimum degree sum of $k$ independent vertices of a graph $G$. A spanning tree with at most $3$ leaves is called a spanning $3$-ended tree. In this paper, we prove that for any $k$-connected claw-free graph $G$ with $|G|=n$, if ${\sigma }_{k+3}(G)\ge n–k$, then $G$ contains a spanning $3$-ended tree.