Cohen-Macaulay 独立复形不可壳化或不可顶点分解的最小例子
Minimal examples of Cohen-Macaulay independence complexes that fail to be shellable or vertex decomposable
- McMaster University（麦克马斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
通过对 11 个顶点上所有连通图的穷举普查，找到了独立复形为 Cohen-Macaulay 但不可壳化或可壳化但不可顶点分解的最小图例子。
AI中文摘要：
我们对所有 $11$ 个顶点上的 $1,006,700,565$ 个连通图进行了穷举普查，以寻找其独立复形为 Cohen-Macaulay 但不可壳化，或可壳化但不可顶点分解的图的最小例子。特别地，当特征不为 2 时，恰好有两个图 $G$ 使得 ${\ m Ind}(G)$ 为 Cohen-Macaulay 但不可壳化，并且恰好有六个图使得 ${\ m Ind}(G)$ 可壳化但不可顶点分解。
英文摘要：
We report on an exhaustive census of all 1,006,700,565 connected graphs on $11$ vertices to find the minimal examples of graphs whose independence complexes are Cohen-Macaulay but not shellable, or shellable but not vertex decomposable. In particular, there are exactly two graphs $G$ where ${\rm Ind}(G)$ is Cohen-Macaulay but not shellable, when the characteristic is not two, and exactly six graphs where ${\rm Ind}(G)$ is shellable but not vertex decomposable.
