Refinements of degree conditions for the existence of a spanning tree without small degree stems

A spanning tree of a graph without vertices of degree 2 is called a homeomorphically irreducible spanning tree (or a HIST) of the graph. Albertson et al. (1990) [1] gave a minimum degree condition for the existence of a HIST, and recently, Ito and Tsuchiya (2022) [11] found a sharp degree-sum condition for the existence of a HIST. In this paper, we refine these results, and extend the first one to a spanning tree in which no vertex other than the endvertices has small degree. (c) 2024 Published by Elsevier B.V.