Spanning trees with at most k leaves in K1,4-free graphs

We obtain a sufficient condition for K1,4-free graphs to have spanning trees with at most k leaves, as a generalization of the condition of Kyaw [A. Kyaw, Spanning trees with at most 3 leaves in K1,4-free graphs, Discrete Math. 309 (2009) 6146-6148] for K1,4-free graphs to have spanning trees with at most 3 leaves.

► We obtain a result for K1,4-free graphs to have spanning trees with at most k leaves. ► This result is a generalization of the condition of Kyaw for K1,4-free graphs to have spanning trees with at most 3 leaves. ► To prove our result, we use the notion of a t-ended system of vertices, paths and cycles in a graph, which was introduced by Win.