On Homeomorphically Irreducible Spanning Trees in Cubic Graphs
Arthur Hoffmann-Ostenhof, Kenta Noguchi, Kenta Ozeki
TL;DR
This paper investigates the existence of homeomorphically irreducible spanning trees (Hists) in cubic graphs, providing necessary conditions and resolving an open question in the field.
Contribution
It offers a necessary condition for the existence of Hists in cubic graphs and answers an open question about their presence.
Findings
Established a necessary condition for Hists in cubic graphs.
Confirmed the existence of Hists in certain cubic graphs.
Resolved an open question on Hists by Albertson et al.
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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Cellular Automata and Applications · Graph Labeling and Dimension Problems