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

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arxiv 2402.18352 v1 pith:UO7LME57 submitted 2024-02-28 cs.DS cs.CGmath.CO

classification cs.DScs.CGmath.CO
keywords classesapproximationpolynomial-timeschemesfractionalfractionallygraphgraphs
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Subdivided expanders and counterexamples to the Tree Product Conjecture

    math.CO 2026-08 accept novelty 7.0 of 10

    For every integer d≥2, the paper constructs graphs of degree-d polynomial growth whose balanced separators are too large by a logarithmic factor to fit in the conjectured product structure.

  2. Layered tree-independence number and clique-based separators

    math.CO 2025-06 conditional novelty 7.0 of 10

    Map graphs, hyperbolic uniform disk graphs, and spherical uniform disk graphs are shown to have bounded or radius-dependent layered tree-independence number, yielding new weighted subexponential algorithms.

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