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- Title
Spanning trees in graphs of high minimum degree with a universal vertex II: A tight result.
- Authors
Reed, Bruce; Stein, Maya
- Abstract
We prove that, if m $m$ is sufficiently large, every graph on m+1 $m+1$ vertices that has a universal vertex and minimum degree at least ⌊2m3⌋ $\lfloor \phantom{\rule[-0.5em]{}{0ex}}\frac{2m}{3}\rfloor $ contains each tree T $T$ with m $m$ edges as a subgraph. Our result confirms, for large m $m$, an important special case of a conjecture by Havet, Reed, Stein, and Wood. The present paper builds on the results of a companion paper in which we proved the statement for all trees having a vertex that is adjacent to many leaves.
- Subjects
TREE graphs; SPANNING trees; LOGICAL prediction
- Publication
Journal of Graph Theory, 2023, Vol 102, Issue 4, p797
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.22899