Hoffmann-Ostenhof, A., Noguchi, K., & Ozeki, K. (2018). On homeomorphically irreducible spanning trees in cubic graphs. Journal of Graph Theory, 89(2), 93–100. https://doi.org/10.1002/jgt.22242
E192-02 - Forschungsbereich Databases and Artificial Intelligence
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Journal:
Journal of Graph Theory
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ISSN:
0364-9024
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Date (published):
Oct-2018
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Number of Pages:
8
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Peer reviewed:
Yes
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Keywords:
Discrete Mathematics and Combinatorics; Geometry and Topology; Bipartite; cubic graph; cyclic edge-connetivity; fullerene; HIST; spanning tree
en
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.
