Spanning trees in dense graphs (Q2777891)

The paper proves the following, almost optimal result: For any \(\delta > 0,\) there exist constants \(c\) and \(n_0\) such that, if \(n \geq n_0,\) \(T\) is a tree of order \(n\) and maximum degree at most \(cn/\log n,\) and graph \(G\) of order \(n\) has minimum degree at least \((1/2+\delta)n,\) then \(T\) is a subgraph of \(G.\) The proof is based on the regularity lemma/blow-up lemma method. One of the main merits is: this is the first case where this proof method was applicable for finding spanning subgraphs with higher than constant maximum degree.