发表机构
Department of Mathematics and Statistics, Acadia University; School of Mathematical and Computational Sciences, University of Prince Edward Island（阿卡迪亚大学数学与统计系; 爱德华王子岛大学数学与计算科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完成了k>4时无H图k着色的极小障碍刻画，证明当且仅当H为P₄+ℓP₁（ℓ≥0）的诱导子图时，k顶点临界无H图仅有有限个。
AI 中文摘要
若图不含与H同构的诱导子图，则称其为无H图。2020年，Chudnovsky、Goedgebeur、Schaudt和Zhong刻画了所有图H，使得无H图的3着色仅有有限个极小障碍。一般而言，无H图的k着色的极小障碍是(k+1)顶点临界无H图，即满足χ(G)=k+1且对G中每个顶点v都有χ(G-v)=k的无H图。本文完成了k>4时的刻画，证明当且仅当H是P₄+ℓP₁（ℓ≥0）的诱导子图时，k顶点临界无H图仅有有限个。
英文摘要
A graph is $H$-free if it has no induced subgraph isomorphic to $H$. In 2020, Chudnovsky, Goedgebeur, Schaudt, and Zhong characterized all graphs $H$ such that there are only finitely many minimal obstructions to $3$-colouring $H$-free graphs. In general, the minimal obstructions to $k$-colouring $H$-free graphs are the $(k+1)$-vertex-critical $H$-free graphs, those are, the $H$-free graphs $G$ with $χ(G)=k+1$ but $χ(G-v)=k$ for every vertex in $G$. In this paper we complete the characterization for all $k > 4$ by showing that there are onky finitely $k$-vertex-critical $H$-free graphs if and only if $H$ is an induced subgraph of $P_4+\ell P_1$ for some $\ell \geq 0$.
