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 \(\sigma_{k+3}(G) \geq n – k\), then \(G\) contains a spanning \(3\)-ended tree.