# 江苏师大70周年校庆系列学术讲座（一百零九）

朱绪鼎，现为浙江师范大学特聘教授、博士生导师，浙江师范大学离散数学研究中心主任。2010年国家级人才计划入选者。研究专长是图论、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。发表论文250余篇，论文被引用2500余次（MathSciNet）。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 Math., Contrib. Discrete Math., Discuss.Math.Graph Theory, Bulletin of  Academia Sinica, Bulletin of Academia, Taiwanese J. Math等国际学术期刊编委。

A list assignment of a graph $G$ assigns to each vertex $v$ a set $L(v)$ of permissible colors. A proper $L$-coloring  of $G$ is a mapping $f$ with $f(v) \in L(v)$ for each vertex and $f(u) \ne f(v)$ for each edge. We are interested in the   problem whether $G$ has a proper $L$-coloring when the list-size $|L(v)|$ for each vertex $v$ is given.Combinatorial Nullstellensatz is a powerful tool in the study of such problems. In this lecture, I will explain how this problem is related to polynomials, how is Combinatorial Nullstellensatz is applied. In particular, I will show the application of this method to the study of list coloring of planar graphs, and prove that every planar graph has Alon-Tarsi number at most 5.

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