Induced packing treewidth
Abstract
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 H be a fixed family of graphs. We define induced-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 H intersecting that bag. This notion generalizes some previously studied parameters: when H=\P1\, it is equivalent to tree-independence number, and when H=\P2\, it is equivalent to induced matching treewidth. We show that bounded induced-H-packing treewidth yields new algorithmic consequences for a range of choices of H. In particular, we prove the following results for graphs of bounded induced-H-packing treewidth. Our results partially answer and substantially extend a question of Bodlaender, Fomin, and Korhonen [SODA~2026] on the tractability of MWIS for graphs of bounded induced-H-packing treewidth for H=\P3\ and for H equal to the family of all cycles.
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