We investigate a relaxation of the notion of treewidth-fragility, namely tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for independent packing problems 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.

翻译：我们研究了树宽脆弱性概念的松弛形式，即树独立数脆弱性。特别地，我们在分数树独立数脆弱图类上获得了独立打包问题的多项式时间近似方案。我们的方法统一并扩展了多个看似无关图类上的已知多项式时间近似方案，例如固定维度中胖物体相交图类或真子式封闭类。我们还研究了分层树独立数这一相关概念，它是分层树宽的松弛形式。