Spanning trees with at most 6 leaves in \(K_{1,5}\)-free graphs (Q2298039)

Summary: A graph \(G\) is called \(K_{1,5}\)-free if \(G\) contains no \(K_{1,5}\) as an induced subgraph. A tree with at most \(m\) leaves is called an \(m\)-ended tree. Let \(\sigma_k \left(G\right)\) be the minimum degree sum of \(k\) independent vertices in \(G\). In this paper, it is shown that every connected \(K_{1,5}\)-free graph \(G\) contains a spanning 6-ended tree if \(\sigma_7 \left(G\right) \geq |G|- 2\).