报告题目：List 4-colouring of planar graphs

报 告 人：朱绪鼎 教授 浙江师范大学

邀请人：张欣 副教授

报告时间：2022年4月19日（周二）14：30-15：30

腾讯会议ID：800 629 462

报告人简介：朱绪鼎，博士，教授，博士生导师，浙江师范大学特聘教授，浙江师范大学离散数学研究中心主任。1991年获加拿大University of Calgary数学博士学位，1991年至1993年在加拿大Simon Fraiser University做博士后研究，1993年至1995年在德国比勒菲尔德大学做博士后研究，1995年加入台湾中山大学应用数学系，先后聘为台湾中山大学特聘研究教授，台湾西湾讲座教授，获得台湾科学委员会杰出研究奖，台湾数学学会学术奖，主持台湾杰出学者研 究计划。2010年全职到浙江师范大学任教。研究专长是图论、演算法和组合优化。主持国家自然科学面上项目4项，浙江省自然科学重点项目1项。在国际SCI期刊发表论文250余篇，论文被引用2700余次（MathSciNet），H-index为26。二十多次应邀在重要的国际学术会议上作大会报告。现任“J. Graph Theory”，“European J. Combin.”，“Discrete. Mathematic”，“Contrib.Discrete Math”，“Discuss. Math. Graph Theory Graph Theory”，“Bulletin of Academia Sinica”，“Taiwanese Journal of Mathematics”等国际学术期刊编委。

报告摘要：It is known that there are planar graphs G and 4-list assignments L of G such that G is not L-colourable. A natural direction of research is to put restrictions on the list assignments so that for any planar graph G and any 4-list assignment L of G satisfying the restrictions, G is L-colourable. One kind of lists studied in the literature is lists with separation. A (k, s)-list assignment of G is a k-list assignment of G with |L(x) ∩ L(y )| ≤ s for each edge xy . A graph G is called (k, s)-choosable if G is L-colourable for any (k, s)-list assignment L of G. Mirzakhani constructed a planar graph G which is not (4, 3)-choosable and Kratochvíl, Tuza and Voigt proved that every planar graph is (4, 1)-choosable. A natural question (asked by Kratochvíl, Tuza and Voigt ) is whether every planar graph is (4, 2)-choosable. This question received a lot of attention, but there were not much progress. Recently, I proved that the answer to this quesiton is positive. In this lecture, I shall sketch the proof.

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