Spanning Trees in Graphs of High Minimum Degree with a Universal Vertex II: A Tight Result

Abstract

We prove that, if $m$ is sufficiently large, every graph on $m+1$ vertices that has a universal vertex and minimum degree at least $\lfloor \frac{2m}{3}\rfloor$ contains each tree $T$ with $m$ edges as a subgraph. Our result confirms, for large $m$, 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.

31 pages

References in corpus (1)

• The approximate Loebl-Komlós-Sós Conjecture IV: Embedding techniques and the proof of the main result

Cited by in corpus (2)

• Maximum and minimum degree conditions for embedding trees
• Degree conditions for embedding trees