题目 ：Average degrees of edge-chromatic critical graphs
摘要：Given a graph G, denote by ∆, and the maximum degree, the average degree and the chromatic index of G, respectively. A simple graph G is called edge-∆-critical if and for every proper subgraph H of G. Vizing in 1968 conjectured that if G is edge-∆-critical, then In this talk, we show a result that improving the best known bound 2(∆+2)/3 obtained by Woodall in 2007 for ∆ ≥ 56. Additionally, Woodall constructed an infinite family of graphs showing his result cannot be improved by well-known Vizing’s Adjacency Lemma and other known edge-coloring techniques. To overcome the barrier, we follow the recoloring technique of Tashkinov trees to expand Vizing fans technique to a larger class of trees.