A note on the independence number, connectivity and [formula omitted]-ended tree

Abstract

A k-ended tree is a tree with at most k leaves. In this note, we give a simple proof for the following theorem. Let G be a connected graph and k be an integer (k≥2). Let S be a vertex subset of G such that αG(S)≤k+κG(S)−1. Then, G has a k-ended tree which covers S. Moreover, the condition is sharp.