On homeomorphically irreducible spanning trees in cubic graphs
Arthur Hoffmann‐Ostenhof, Kenta Noguchi, Kenta Ozeki · Journal of Graph Theory · 2018
Abstract A spanning tree without a vertex of degree two is called a HIST, which is an abbreviation for homeomorphically irreducible spanning tree. We provide a necessary condition for the existence of a HIST in a cubic graph. As one consequence, we answer affirmatively an open question on HISTs by Albertson, Berman, Hutchinson, and Thomassen. We also show several results on the existence of HISTs in plane and toroidal cubic graphs.