报告人简介：
陈冠涛教授是杰出的图论学家，在图的圈、连通度、着色等经典主题上做出了大量优秀的工作，解决了很多别人提出的有基本重要性的难题，受到同行广泛的尊敬。陈教授学术趣味高雅，研究成果精彩。
陈教授现在是著名学术杂志 Graphs and Combinatorics 的执行主编，是数学和统计系的杰出教授（Distinguished Professor）， 是系主任。

报告内容简介：
Let G be a simple graph. Denote by、Delta(G), delta(G), and k’(G) the maximum degree,
minimum degree and the chromatic index of G. A graph G is edge-Delta-critical if k’(G) =
Delta + 1 and k’(H)<=Delta for any proper subgraph of H of G. Let d(G) denote the average
degree of G. Vizing in 1968 conjectured that the d(G)>=Delta-1 +3/n if G is an edge-Delta-critical graph of order n. We show that if G is an edge-Delta-critical graph with Delta >= 16, then d(G)>=3Delta/4-8. Moreover, we show that there exist two functions D and d such that for any positive real number t in (0; 1), if G is an edge-Delta-critical graph with Delta>=Delta(t) and delta(G)>= d(t), then d(G)>= (1-t)Delta. We will give two
specific functions satisfying the statement above. By using this theorem, we also show that an edge-Delta-critical graph G has d(G)>=Delta-o(Delta ) if delta(G)>= (log Delta )^{3/4}..

主持人：詹兴致 教授
主办单位：数学科学学院 科技处