Prof. Ervin Gyori, gave a lecture titled “On the number of edge-disjoint triangles in K4-free graphs”at AMSS on 27, June, 2017.
In this talk, the main result is the proof of quarter of a century old conjecture of Erdos 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 would be presented too, starting with the clique decomposition conjecture of Katona and Tarjan ('76), and the conjecture of Erdos ('71) when K4-freeness was not assumed. Versions related to other Turan numbers was discussed too. In the proof, they used a nice lemma of Sh. Huang and L. Shi ('14). The main result was a joint work with B. Keszegh.
Ervin Gyori is a professor at Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, interested in graph theory, extremal combinatorics and discrete math. He was nominated for membership of the Hungarian Academy of Sciences.