发表机构
Yokohama National University（横滨国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对2-连通图，证明了亚线性最小度条件可保证其包含所有阶数从4到n的2-连通子图，填补了相关研究的空白。
AI 中文摘要
受泛圈性类似问题的启发，我们研究确保n阶2-连通图G包含阶数为ℓ∈{4,5,…,n}的2-连通子图的最小度条件。Yin和Wu在《Discrete Appl. Math.》387卷（2026年）的论文中首次研究该问题，证明δ(G)≥⌈n/3⌉+1是充分条件。Kashima猜想δ(G)≥√(3n)是充分条件。本文证明，所有n阶2-连通图G，若δ(G)≥2n^(2/3)+6n^(1/3)+2，则必包含从4到n的所有阶数的2-连通子图，这是首个关于n的亚线性阶的充分最小度条件。
英文摘要
Motivated by an analogue of pancyclicity, we study minimum-degree conditions ensuring that a $2$-connected graph $G$ of order $n$ contains a $2$-connected subgraph of every order $\ell\in\{4,5,\ldots,n\}$. Yin and Wu [A minimum degree condition for a 2-connected graph containing all possible orders of 2-connected subgraphs, Discrete Appl. Math. 387 (2026), 129-136] initiated the study of this problem and showed that the condition $δ(G)\ge \lceil n/3\rceil+1$ is sufficient. Kashima conjectured that the condition $δ(G)\ge \sqrt{3n}$ is sufficient. In this paper, we prove that every $2$-connected graph $G$ of order $n$ with $δ(G)\ge 2n^{2/3}+6n^{1/3}+2$ contains a $2$-connected subgraph of every order from $4$ to $n$. In particular, this gives the first sufficient minimum-degree condition of sublinear order in $n$.
Comments5 pages
