Tianchi Yang, On the maximum number of edges in k-critical graphs

In this talk, we will discuss the problem of determining the maximum number of edges in an n-vertex k-critical graph. A graph is considered k-critical if its chromatic number is k, but any proper subgraph has a chromatic number less than k. The problem remains open for any integer k ≥ 4. Our presentation will showcase an improvement on previous results achieved by employing a combination of extremal graph theory and structural analysis. We will introduce a key lemma, which may be of independent interest, as it sheds light on the partial structure of dense k-critical graphs. This is joint work with Cong Luo and Jie Ma.