報(bào)告人：樊丹丹 講師
報(bào)告題目：Spectral radius and edge-disjoint spanning trees of graphs with prescribed edge connectivity
報(bào)告時(shí)間：2026年6月8日（周一）下午14:30
報(bào)告地點(diǎn)：騰訊會(huì)議：537764142
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
樊丹丹，新疆農(nóng)業(yè)大學(xué)，講師，2024年6月博士畢業(yè)于華東理工大學(xué)，研究方向是圖譜理論。主持國(guó)家自然科學(xué)基金青年基金及自治區(qū)自然科學(xué)基金青年基金各一項(xiàng)。近5年來(lái)，在《Journal of Graph Theory》、《European Journal of Combinatorics》、《Electron. J. Combin.》等SCI源期刊上發(fā)表學(xué)術(shù)論文20余篇。
報(bào)告摘要：
The spanning tree packing number of a graph $G$, denoted by $\tau(G)$, is the maximum number of edge-disjoint spanning trees contained in $G$. The study of $\tau(G)$ is one of the classic problems in graph theory. A famous theorem of Tutte and Nash-Williams implies that the edge connectivity $\kappa'(G)$ and $\tau(G)$ are closely related with $\tau(G)\ge \lfloor \tfrac{\kappa'(G)}{2}\rfloor$. Therefore, it is interesting to explore conditions on a graph $G$ with $\kappa'(G)\le 2k-1$ to ensure $\tau(G)\ge k$. In this talk, we establish spectral radius conditions to ensure $\tau(G)\geq k$ in $k$-edge-connected graphs with fixed minimum degree.