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：有界膨胀的概念为捕捉具有重要算法性质的稀疏图类提供了一种稳健的方法。最值得注意的是，每个可用一阶逻辑定义的问题都能在有界膨胀图类上以线性时间求解。稀疏图类的一阶解释与转换会产生更一般的稠密图类，这些图类似乎继承了其稀疏对应物的许多优良算法性质。本文表明，我们可以通过有界膨胀类的有限膨胀分解、灌木分解和奇偶分解来编码具有结构有界膨胀的类中的图。这些分解有助于将性质从稀疏图类提升到结构稀疏图类。