题  目：Chromatic polynomials of hypergraphs

报告人： 董峰明 教授  新加坡南洋理工大学

邀请人： 邓青英 老师  湘潭大学新2会员管理端10888

摘  要：A hypergraph H consists of two finite sets V and E, called the vertex set and edge set of H, where each element of E is a subset of V . If |e| = 2 holds for each e ∈ E, then H is a graph. The vertex coloring of hypergraphs was introduced by Erdȍs and Hajnal in 1966. For any positive integer k, a proper k-coloring of H is a mapping ϕ from V to {1, 2, · · · , k} such that |{ϕ(v) : v ∈ e}| ≥ 2 holds for each e ∈ E. Clearly, if |e| ≥ 2 for each e ∈ E, then H admits a proper k-coloring for every k ≥ |V |. The chromatic polynomial of H is defined to be the polynomial, denoted by P(H, x), such that P(H, k) counts the number of proper k-colorings of H whenever k is a positive integer. Clearly, if H is a graph G, then P(H, k) is exactly the chromatic polynomial of G.

In this talk, I will introduce some basic properties, known results and open problems of the chromatic polynomials of hypergraphs.

报告人简介：

董峰明教授，新加坡南洋理工大学博士生导师，图论领域（特别是图多项式不变量领域）著名专家。主要研究兴趣包括图与超图的多项式和拟阵、着色、生成树、匹配、极值图等。目前与他人合作撰写出版专著和大学教材5部，由新加坡世界科学出版公司出版；在国际性数学刊物上发表了约80多篇论文，部分文章发表在Journal of Combinatorial Theory Series A、Journal of Combinatorial Theory Series B、Journal of graph Theory、European Journal of Combinatorics、SIAM Journal on Discrete Mathematics等图论与组合学的顶级刊物上；董峰明教授解决了若干公开猜想，其中比较有影响的是牛津大学Dominic Welsh教授提出的关于着色多项式的The Shameful Conjecture.

时  间：2021年12月 20日（周一）上午10：00—12：00

地  点：数学南楼103室，腾讯会议ID：882811289

欢迎广大师生参加！