报告题目：Real-rootedness of independence polynomials

报告人：刘丽

负责人：李雪珊

报告时间：2025年10月09日09：00-10:00

报告地点：腾讯会议，会议号：219 671 659

参加人员：教师，研究生

报告摘要：Motivated by the conjecture of Alavi, Malde, Schwenk and Erdos, there are families of graphs, whose independence polynomials is unimodal, and furthermore is real-rooted. For example, Chudnovsky and Seymour obtained that the independence polynomial of all claw-free graphs has only real roots. Then it is natural to construct graphs with claw having real-rooted independence polynomials. In this paper, following the idea of Zhu et al., we introduce infinite graphs based on the rooted-product, whose independence polynomials have only real roots. Our results not only make progress on the conjecture of Alavi, Malde, Schwenk and Erdos, but also generalize Zhu et al.'s results.

报告人简介：刘丽，教授，博士生导师。霍英东青年教师奖获得者，山东省泰山学者青年专家。主要从事多项式零点分布、矩阵全正性和组合不等式的研究。在AAM, JAC等数学期刊上发表论文20余篇，所取得的成果被算法分析之父D.E. Knuth（高德纳）写入其经典巨著《The Art of Computer Programming》Vol.4B等多部专著中。主持国家自然科学基金项目4项。作为第一完成人荣获山东省自然科学三等奖和山东省高等学校科学技术奖一等奖各1项。