Erdős and Sésg conjectured in 1963 that if \(G\) is a graph of order \(p\) and size \(q\) with \(q > \frac{1}{2}p(k-1)\), then \(G\) contains every tree of size \(k\). This is proved in this paper when the girth of the complement of \(G\) is greater than \(4\).