Spanning Trees in Dense Graphs

Abstract

In this paper we prove the following almost optimal theorem. For any δ > 0, there exist constants c and n 0 such that, if n [ges ] n 0 , T is a tree of order n and maximum degree at most cn /log n , and G is a graph of order n and minimum degree at least (1/2 + δ) n , then T is a subgraph of G .