The concept of bounded expansion provides a robust way to capture sparse graph classes with interesting algorithmic properties. Most notably, every problem definable in first-order logic can be solved in linear time on bounded expansion graph classes. First-order interpretations and transductions of sparse graph classes lead to more general, dense graph classes that seem to inherit many of the nice algorithmic properties of their sparse counterparts. In this paper, we show that one can encode graphs from a class with structurally bounded expansion via lacon-, shrub- and parity-decompositions from a class with bounded expansion. These decompositions are useful for lifting properties from sparse to structurally sparse graph classes.

翻译：有界扩张概念提供了一种鲁棒的途径来刻画具有有趣算法性质的稀疏图类。最值得注意的是，一阶逻辑可定义的每个问题都能在有界扩张图类上以线性时间求解。稀疏图类的一阶解释与转导产生更一般的稠密图类，这些图类似乎继承了其稀疏对应类别的许多优良算法性质。在本文中，我们证明可以通过来自有界扩张类的lacon-、shrub-与奇偶性分解来编码具有结构有界扩张的图类中的图。这些分解有助于将性质从稀疏图类提升到结构稀疏图类。