SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 431-469, January 2020.
A graph is $H$-free if it has no induced subgraph isomorphic to $H$. We characterize all graphs $H$ for which there are only finitely many minimal non-3-colorable $H$-free graphs. Such a characterization was previously known only in the case when $H$ is connected. This solves a problem posed by Golovach et al. As a second result, we characterize all graphs $H$ for which there are only finitely many $H$-free minimal obstructions for list 3-colorability.

中文翻译：

---

三色和列出三色无$ H $图的障碍

SIAM离散数学杂志，第34卷，第1期，第431-469页，2020年1月。
如果图形没有与$ H $同构的诱导子图，则该图形将不含$ H $。我们对所有图$ H $进行特征化，对于这些图，只有有限的最小无三色非$ H $图。以前仅在连接$ H $时才知道这种特征。这解决了Golovach等人提出的问题。第二个结果是，我们对所有图表$ H $进行了特征分析，对于列表3的可着色性，只有有限的许多$ H $无最小障碍物。