主讲人：何家林 青年研究员（华东师范大学）
主持人：叶青杰 讲师
时 间：2026年10月28日 13:00-13:40
地 点：数学楼102报告厅
报告内容介绍：
Erdős asked whether for any n-vertex graph G, the parameter p∗G=min_{i≥1} |V(G_i)|−1 is at most n^2/4, where the minimum is taken over all edge decompositions of G into edge-disjoint cliques G_i. In a restricted case, Győri and Keszegh roved that p∗G≤n^2/4 for all K4-free graph G. Motivated by their proof approach, they conjectured that for any n-vertex K4-free graph G with e edges, and any greedy partition P of G of size r, the number of triangles in G is at least r(e−r(n−r)). If true, this would imply a stronger bound on p∗G. We disprove their conjecture by constructing infinitely many counterexamples with arbitrarily large deviations. We further establish a corrected lower bound on the number of triangles in such graphs, which recovers the conjectured bound once the small counterexamples we identify are excluded. This is a joint work with Jie Ma, Yan Wang, and Chunlei Zu.
主讲人介绍：