SPANNING K-ENDED TREES OF A CLAW-FREE GRAPH
For a tree T, a vertex of T with degree one is often called a leaf of T. Let be an integer. We prove that if a connected claw-free graph G satisfies then G has a spanning tree having at most k leaves, where denotes the maximum number of vertices of G that are pairwise distance at least three in G. This result implies a known result proved by Kano et al. [5] which states that if the minimum degree sum of independent vertices of a connected claw-free graph G is at least then G has a spanning k-ended tree. The condition on is sharp.
spanning tree, claw-free graph, leaf, k-ended tree.