分数树独立数脆弱图上的诱导子图问题的多项式时间近似方案
Polynomial-time approximation schemes for induced subgraph problems on fractionally tree-independence-number-fragile graphs
AI总结：
本文提出分数树独立数脆弱图类上的多项式时间近似方案，统一扩展了多类图的结果，并研究分层树独立数用于精确亚指数算法。
摘要：
我们研究了分数树宽脆弱性概念的松弛，即分数树独立数脆弱性。特别地，对于满足给定$\mathsf{CMSO}_2$公式的最大权重稀疏诱导子图等元问题，我们在分数树独立数脆弱图类上获得了多项式时间近似方案。我们的方法统一并扩展了若干看似无关图类上的已知多项式时间近似方案，例如固定维度中胖物体交集图类或真minor闭类。我们还研究了分层树独立数这一相关概念，它是分层树宽的松弛，并探讨了其在精确亚指数时间算法中的应用。
英文摘要：
We investigate a relaxation of the notion of fractional treewidth-fragility, namely fractional tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for meta-problems such as finding a maximum-weight sparse induced subgraph satisfying a given $\mathsf{CMSO}_2$ formula on fractionally tree-independence-number-fragile graph classes. Our approach unifies and extends several known polynomial-time approximation schemes on seemingly unrelated graph classes, such as classes of intersection graphs of fat objects in a fixed dimension or proper minor-closed classes. We also study the related notion of layered tree-independence number, a relaxation of layered treewidth, and its applications to exact subexponential-time algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
