Alon-Tarsi number of line graphs
报告题目(Title)：Alon-Tarsi number of line graphs
报告人(Speaker)：朱绪鼎 教授（浙江师范大学）
地点(Place)：腾讯会议 ID： 431 862 149 | 密码：753856
时间(Time)：2026年 10月9日（周五）16:00-17:00
邀请人(Inviter)：徐敏
报告摘要
Let G be a multigraph and L(G) be the line graph of G. Let $P_{L(G)}(x_e : e \in E(G)) = \prod_{ee' \in E(L(G)), e < e'} (x_e - x_{e'})$ be the graph polynomial of L(G) (where < is an arbitrary linear order of E(G)). The Alon-Tarsi number of L(G), denoted by AT'(G), is the minimum integer k such that $P_{L(G)}$ has a non-vanishing monomial $\prod_{e \in E(G)} x_e^{t(e)}$ with t(e) < k for all $e \in E(G)$. It follows from Combinatorial Nullstellensatz that for any graph G, $\chi'_\ell(G) \le AT'(G)$, where $\chi'_\ell(G)$ is the list chromatic index of G. For a simple graph G and a positive integer r, let $G^{(r)}$ be the multigraph obtained from G by replacing each edge with r parallel edges. It was proved by Seymour that for any series-parallel multigraph G, $\chi'(G) = \max\{\Delta(G), \lceil \Gamma(G) \rceil\}$, where $\Gamma(G) = \max\{ \frac{2|E(H)|}{|V(H)|-1} : H \subseteq G, |V(H)| \text{ is odd} \}$. Juvan, Mohar and Thomas proved that if G is a simple series-parallel graph, then $\chi'_\ell(G) = \chi'(G)$. We prove that if G is a series-parallel multigraph with all the edges having the same multiplicity, then $AT'(G) = \chi'(G)$. We conjecture that the same equality holds for all series-parallel multigraphs. This is a joint work with Chenglong Deng.
主讲人简介
朱绪鼎，1991年获得加拿大卡尔加里大学数学博士学位。曾任中国台湾中山大学西湾讲座教授。2010年入选第三期国家高端人才计划，任职于浙江师范大学。现任浙江师范大学数学学院教授，浙江师范大学离散数学研究中心主任。主要研究方向是图的染色。现（曾）任《J. Graph Theory》, 《SIAM J. Discrete Mathematics》，《Electronic J. Combin.》，《European J. Combin.》，《Discrete. Mathematics》，《Contrib. Discrete Math.》，《Taiwanese J. Mathematics》，《Discuss. Math. Graph Theory》，《Bulletin of Academia Sinica》，《Czechoslovak Mathematical Journal》，《Indian J. Disc. Math.》等国际学术期刊编委。发表SCI论文300余篇，其中JCTB 27 篇，Combinatorica 8篇， JGT 66篇，被引用3600余次（MathSciNet）。三十余次应邀在国际学术会议做大会报告。
