Degree sum conditions for the existence of homeomorphically irreducible spanning trees

In 1990, Albertson, Berman, Hutchinson, and Thomassen proved a theorem which gives a minimum degree condition for the existence of a spanning tree with no vertices of degree 2. Such a spanning tree is called a homeomorphically irreducible spanning tree (HIST). In this paper, we prove that every grap...

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Bibliographic Details
Published in:Journal of graph theory 2022-01, Vol.99 (1), p.162-170
Main Authors: Ito, Taisei, Tsuchiya, Shoichi
Format: Article
Language:English
Subjects:
Apexes
Existence theorems
Graph theory
homeomorphically irreducible spanning tree
spanning tree
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Summary:In 1990, Albertson, Berman, Hutchinson, and Thomassen proved a theorem which gives a minimum degree condition for the existence of a spanning tree with no vertices of degree 2. Such a spanning tree is called a homeomorphically irreducible spanning tree (HIST). In this paper, we prove that every graph of order n ( n ≥ 8) contains a HIST if d ( u ) + d ( v ) ≥ n − 1 for any nonadjacent vertices u and v. The degree sum condition is best possible.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22732