短课程： Polynomial Method in Graph Theory

课程简介：

This series of lectures discuss the application of Combinatorial Nullstellensatz to various problems

in graph theory. We shall present proofs of Combinatorial Nullstellensatz. Give examples of various

problems in graph theory that can be expressed in the language of polynomials. Discussmethods for

 the calculation of coefficients of monomials of polynomials associated to these problems.

These include Alon-Tarsi Theorem, permanent method and partial derivative method. These methods

are explained by various examples. We shall show how to use the method to prove that the four colour

theorem is equivalent to the statement that bridgeless cubic planar graphs are 3-edge choosable.

Show that planar graphs have Alon-Tarsinumber at most 5. The method is applied to the study to total

weight choosability of graphs, andto show that every graph is (2,3)-choosable. Some of the applications

are new research results.

Also some open problems will be discussed in the lectures.

授课教师：朱绪鼎，浙江师范大学教授，第三批国家“”入选者。图论与组合优化研究领域的著名专家，在图的染色理论、结构分析、演算法等领域做出了杰出的贡献，取得一系列重大研究成果，特别是创新发展了图的圆染色理论，使得该方向已成为当前国内外研究的热点之一。朱绪鼎曾先后在国际重要学术刊物上发表SCI研究论文130余篇，论文被同行引用1000余次。2007年，在ISI公布的、有全球900多位数学家入选的世界数学家被引用次数排名中，位列第67名。European Journal of Combinatorics, SIAM Journal on Discrete Mathematics,Journal of Graph Theory,Discrete Mathematics等杂志编委。

授课时间：2018年6月4日-6月15日

授课安排：

6月4日56节：海韵教学楼403

6月6日12节：数学物理大楼661

6月8日12节：数学物理大楼661

6月11日56节：海韵教学楼403

6月13日12节：数学物理大楼661

6月15日12节：数学物理大楼661

欢迎各位同学参加！