中文摘要：

A spanning tree with no more than 3 leaves is called a spanning 3-ended tree.In this paper, we prove that if G is a k-connected（k ≥ 2） almost claw-free graph of order n and σk+3（G） ≥ n + k + 2, then G contains a spanning 3-ended tree, where σk（G） =min{∑v∈Sdeg（v） : S is an independent set of G with |S| = k}.

英文摘要：

A spanning tree with no more than 3 leaves is called a spanning 3-ended tree. In this paper, we prove that if G is a k-connected （k≥ 2） almost claw-free graph of order n and σk＋3（G） ≥ n ＋ k ＋ 2, then G contains a spanning 3-ended tree, where σk（G） = min{∑es deg（v） ： S is an independent set of G with ｜S｜ = k}.