Abstract: | The main result is the proof of quarter of a century old conjecture ofErdos that every K4-free graph with n vertices and t2(n)+ k edges contains k pairwise edge disjoint triangles where t2(n) is the two-partite Turan number. The 50 year history and preliminaries of this conjecture will be presented too,starting with the clique decomposition conjecture of Katona and Tarjan ('76), and the conjecture of Erdos ('71) when K4-freeness is not assumed. Versions related to other Turan numbers will be discussed too. In the proof, we used a nice lemma of Sh. Huang and L. Shi ('14). The main result is a joint work with B. Keszegh. 简历:Ervin Gyori is a professor at Alfred Renyi Institute of Mathematics,Hungarian Academy ofSciences, interested in graph theory, extremal combinatorics and discrete math. He was nominated formembership of the Hungarian Academy of Sciences. |