A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree at least three. In this paper, we show a degree condition for a claw-free graph to have spanning trees with at most five branch vertices and leaves in total. Moreover, the degree sum condition is best possible.
Y. Chen, P. H. Ha and D. D. Hanh. Spanning trees with at most 4 leaves in K1,5-free graphs. Discrete Math, 342:2342-2349, 2019.
R. Gould, W. Shull. On spanning trees with few branch vertices. Discrete Math, 343:111581, 2020.
M. Kano, A. Kyaw, H. Matsuda, K. Ozeki, A. Saito and T. Yamashita. Spanning trees with a bounded number of leaves in a claw-free graph. Ars Combinatoria, 103:137-154, 2012.
A. Kyaw. Spanning trees with at most k leaves in K1,4-free graphs. Discrete Math, 311:21352142, 2011.
H. Matsuda, K. Ozeki and T. Yamashita. Spanning trees with a bounded number of branch vertices in a claw-free graph. Graphs and Combinatorics, 30:429-437, 2014.
S. Maezawa, R. Matsubara and H. Matsuda. Degree conditions for graphs to have spanning trees with few branch vertices and leaves. Graphs and Combinatorics, 35:231-238, 2019.
ZhG. Nikoghosyan. Spanning trees with few branch and end vertices. Math. Probl. Comput. Sci, 46:15-28, 2016.
A. Saito and K. Sano. Spanning trees homeomorphic to a small tree. Discrete. Math, 339:677681, 2016.
P. Wang and J. Cai. Spanning trees with at most 4 leaves in k1,5-free graphs. Discrete Math, 342:1546-1552, 2019.