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arXiv · 2402.18352

Polynomial-time approximation schemes for induced subgraph problems on fractionally tree-independence-number-fragile graphs

Esther Galby·Andrea Munaro·Shizhou Yang
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Abstract

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.

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Esther Galby, Andrea Munaro, Shizhou Yang. 2024-02-28. Polynomial-time approximation schemes for induced subgraph problems on fractionally tree-independence-number-fragile graphs. https://arxiv.org/abs/2402.18352

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