Spanning trees of claw-free graphs with few leaves and branch vertices

Let T be a tree. A vertex of degree one is a leaf of T and a vertex of degree at least three is a branch vertex of T. A graph is said to be claw-free if it does not contain K1,3 as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of claw-free graphs. Applying the main results, we also give some improvements of previous results on the spanning trees with few branch vertices for the case of claw-free graphs. arXiv admin note: text overlap with arXiv:2201.01043