发表机构
Center for Discrete Mathematics, Fuzhou University（福州大学离散数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究无孤立顶点的\(n\)顶点二分图中最小局部平均度与全局平均度之比的最大值，通过证明得出\(F_{\mathrm{bip}}(n)=\frac14\sqrt n+\frac38+o(1)\)，回答了图扎的问题。
AI 中文摘要
设\(F_{\mathrm{bip}}(n)\)为所有无孤立顶点的\(n\)顶点二分图中最小局部平均度与全局平均度之比的最大值。我们证明\(F_{\mathrm{bip}}(n)=\frac14\sqrt n+\frac38+o(1)\)。这回答了图扎提出的一个问题。
英文摘要
Let $F_{\mathrm{bip}}(n)$ denote the maximum, over all $n$-vertex bipartite graphs without isolated vertices, of the ratio of the minimum local average degree to the global average degree. We prove that $F_{\mathrm{bip}}(n)=\frac14\sqrt n+\frac38+o(1)$. This answers a problem posed by Tuza. The lower bound is obtained from a new family of bipartite constructions, while the upper bound is proved by a new algebraic approach, different from the combinatorial methods used previously. The key ingredient is a spectral argument based on a normalized biadjacency matrix.
Comments13 pages
