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We investigate a relaxation of the notion of treewidth-fragility, namelytree-independence-number-fragility. In particular, we obtain polynomial-timeapproximation schemes for independent packing problems on fractionallytree-independence-number-fragile graph classes. Our approach unifies andextends several known polynomial-time approximation schemes on seeminglyunrelated graph classes, such as classes of intersection graphs of fat objectsin a fixed dimension or proper minor-closed classes. We also study the relatednotion of layered tree-independence number, a relaxation of layered treewidth.

Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs