A Result of Erdos-Sos Cojecture

Wang Min1, Li Guo-jun2, Liu Ai-de3
1Department of Mathematics Yantai University Yantai 264005, China
2Department of Mathematics and Systems Science Shandong Unniversity Jinan 250100, China
3Department of Mathematics Yantai Teachers’ College Yantai 264025, China

Abstract

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 \(4\).