报告题目：Existence of trees with prescribed maximum degrees and spectral radii

报告人：董峰明教授，南洋理工大学

报告时间：2026年6月4日（周四）15:00-18:00

报告地点：20-308

报告摘要：In this talk, I will introduce my recent work joint with Dr. Zhang Ruixue from Qingdao University. For any positive integer r and positive number α, let Wr(α) denote the set of non-negative numbers defined recursively: α∈Wr(α), and for any multi-set qi∈Wr(α):qi>0,1≤i≤s,β:=α−i=1  belongs to Wr(α) as long as β≥0, where 1≤s0, and 1≤s≤r otherwise. We first show that 0∈Wr(α) if and only if there exists a tree T with the property that its maximum degree Δ(T) is at most r and spectral radius λ(T) is equal to α. It follows that the set of spectral radii of non-trivial trees is exactly the set of positive numbers α such that 0∈W⌊α2⌋(α). Applying this conclusion, we prove that for any positive integers r and k, there exists a tree T with Δ(T)=r and λ(T)=k if and only if14k+1<r≤k.

报告人简介：董峰明教授，1997年于新加坡国立大学获博士学位，任教于南洋理工大学，是图多项式领域的国际著名专家。在图多项式、染色、匹配、生成树等图论与组合数学的很多领域作出了重要工作，解决了若干公开猜想，其中比较有影响力的是牛津大学Dominic Welsh教授提出的关于着色多项式的The Shameful Conjecture。在J. Combin. Theory Ser. B，J. Combin. Theory Ser. A，Combin. Probab. Comput.，SIAM J. Discrete Math.，J. Graph Theory等组合图论领域重要杂志上发表论文多篇。

邀请人：朱绪鼎