We prove that, if m is sufficiently large, every graph on m+1 vertices
that has a universal vertex and minimum degree at least β32mββ 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.Comment: 29 page