发表机构
University of Waterloo; Massachusetts Institute of Technology; University of California, Berkeley（滑铁卢大学; 麻省理工学院; 加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于强完美图定理，刻画了|H|≤2时不含H诱导子图的图为c-顶点可删完美图的情况，并将结果扩展到完美图的多个子类。
AI 中文摘要
若图G的每个诱导子图H都满足ω(H)=χ(H)，则称G是完美图。2002年，Chudnovsky、Robertson、Seymour和Thomas成功证明了强完美图定理。受完美图类的这种禁用诱导子图刻画以及对完美图高效算法可能进行扩展的启发，我们研究几乎完美图的结构。我们称一个图是c-顶点可删完美图，若存在常数c个顶点，删除这些顶点后剩余的图是完美图。在本文中，我们刻画了满足|H|≤2的图集合H的类，使得存在自然数c，每个不含H诱导子图的图都是c-顶点可删完美图。我们还将这些结果扩展到完美图的多个著名子类，包括弦图、区间图、分裂图、二分图和完全多部图。
英文摘要
A graph $G$ is perfect if $ω(H) = χ(H)$ for each induced subgraph $H$ of $G$. In 2002, Chudnovsky, Robertson, Seymour, and Thomas famously proved the Strong Perfect Graph Theorem. Motivated by this forbidden induced subgraph characterization of the class of perfect graphs as well as the possible extension of efficient algorithms on perfect graphs, we consider the structure of graphs that are almost perfect. We say a graph is $c$-apex perfect if there is a constant $c$ number of vertices such that, upon the deletion of these vertices, what remains is a perfect graph. In this paper, we characterize the class of the sets of graphs $\mathcal{H}$ with $|\mathcal{H}|\leq 2$ for which there exists $c \in \mathbb{N}$ with the property that each $\mathcal{H}$-free graph is $c$-apex perfect. We also extend these results to several notable subclasses of perfect graphs, including chordal, interval, split, bipartite, and complete multipartite graphs.
