Spanning trees with a bounded number of leaves in a claw-free graph
Mikio Kanō, Aung Kyaw, Haruhide Matsuda, Kenta Ozeki, Akira Saito, Tomoki Yamashita · Ars Combinatoria · 2012
For a graph H and an integer k ≥ 2, let σk(H) denote the minimum degree sum of k independent vertices of H. We prove that if a connected claw-free graph G satisfies σk+1(G) ≥ |G| − k, then G has a spanning tree with at most k leaves. We also show that the bound |G| − k is sharp and discuss the maximum degree of the required spanning trees.