## Some recent progress towards the overfull conjecture

### Songling Shan — Illinois State University

Let G be a simple graph with maximum degree Delta(G). A subgraph H of G is overfull if |E(H)|>Delta(G) is greater than the floor function of |V(H)|/2. Chetwynd and Hilton in 1985 conjectured that a graph G with \Delta(G)>|V(G)|/3 has chromatic index \Delta(G) if and only if G contains no overfull subgraph. In this talk, we will survey some recent progress towards the conjecture. In particular, we will mention the confirmation of the conjecture on graphs with a small core degree, dense quasi-random graphs of odd order, and large graphs of order 2n and minimum degree at least (1+\varepsilon)n for any 0<\varepsilon<1.