发表机构
Department of Computer Science, Shanghai Jiao Tong University（上海交通大学计算机系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一个33顶点、4正则且4连通的图，围长为4，Charney-Davis曲率为1，无合法系统，解决了Jankiewicz等人提出的问题，关键利用限制定理保持障碍。
AI 中文摘要
在2021年的一篇论文中，Jankiewicz、Norin和Wise提出了一个问题：是否存在一个有限的、围长至少为4且Charney-Davis曲率非负的4连通图，使得其没有任何4连通普通子图允许一个合法系统。我们通过从六角棱柱出发，并沿两两不相交的诱导4环附加三个基于$K_{3,4}$的帽来构造这样的图。关键的结构输入是一个限制定理，表明在诱导4环融合上的合法系统限制到每一侧，因此负曲率棱柱所携带的障碍在附加后仍然存在。所得的33顶点图是4正则且4连通的，围长为4，Charney-Davis曲率为1，并且由于4正则性，它是其自身唯一的4连通普通子图。
英文摘要
In a 2021 paper, Jankiewicz, Norin, and Wise asked whether there exists a finite $4$-connected graph of girth at least four and nonnegative Charney--Davis curvature such that no $4$-connected ordinary subgraph admits a legal system. We construct such a graph by starting from the hexagonal prism and attaching three $K_{3,4}$-based caps along pairwise disjoint induced $4$-cycles. The key structural input is a restriction theorem showing that a legal system on an induced-$4$-cycle amalgam restricts to each side, so the obstruction carried by the negatively curved prism survives the attachments. The resulting $33$-vertex graph is $4$-regular and $4$-connected, has girth four and Charney--Davis curvature one, and, by $4$-regularity, is its own unique $4$-connected ordinary subgraph.
