诱导填充树宽
Induced packing treewidth
浏览论文内容
中文总结 AI 辅助
研究引入诱导\(\mathcal{H}\) - 填充树宽框架，统一不同定义的图类，该参数推广了先前参数，证明有界此参数对特定\(\mathcal{H}\)选择有新算法结果，部分回答并扩展了关于最大权独立集可处理性问题。
中文摘要 AI 辅助
本文介绍了一个框架，旨在统一由禁止诱导子图或诱导子式定义的类与由某些结构化树分解的存在定义的类。设\(\mathcal{H}\)为固定的图族，定义了“诱导\(\mathcal{H}\) - 填充树宽”，这是一个基于树分解的图参数，对于每个包，测量与该包相交的\(\mathcal{H}\)中图的成对反完全诱导副本的最大数量。该概念推广了一些先前研究的参数，当\(\mathcal{H}=\{P_1\}\)时等同于树独立数，当\(\mathcal{H}=\{P_2\}\)时等同于诱导匹配树宽。表明有界的诱导\(\mathcal{H}\) - 填充树宽对一系列\(\mathcal{H}\)的选择产生新的算法结果，特别是对于有界诱导\(\mathcal{H}\) - 填充树宽的图证明了一些结果，部分回答并大幅扩展了Bodlaender、Fomin和Korhonen关于\(\mathcal{H}=\{P_3\}\)以及\(\mathcal{H}\)为所有圈族的有界诱导\(\mathcal{H}\) - 填充树宽图上最大权独立集可处理性的问题。
英文摘要
In this paper, we introduce a framework that aims to unify classes defined by forbidden induced subgraphs or induced minors with classes defined by the existence of certain structured tree decompositions. Let $\mathcal{H}$ be a fixed family of graphs. We define \emph{induced-$\mathcal{H}$-packing treewidth}, a tree-decomposition-based graph parameter that, for each bag, measures the maximum number of pairwise anticomplete induced copies of graphs from $\mathcal{H}$ intersecting that bag. This notion generalizes some previously studied parameters: when $\mathcal{H}=\{P_1\}$, it is equivalent to tree-independence number, and when $\mathcal{H}=\{P_2\}$, it is equivalent to induced matching treewidth. We show that bounded induced-$\mathcal{H}$-packing treewidth yields new algorithmic consequences for a range of choices of $\mathcal{H}$. In particular, we prove the following results for graphs of bounded induced-$\mathcal{H}$-packing treewidth. Our results partially answer and substantially extend a question of Bodlaender, Fomin, and Korhonen [SODA~2026] on the tractability of \textsc{MWIS} for graphs of bounded induced-$\mathcal{H}$-packing treewidth for $\mathcal{H}=\{P_3\}$ and for $\mathcal{H}$ equal to the family of all cycles.
