一句话：引入 lacon- 与 shrub-分解，刻画有界扩张图类的一阶转导，并给出其 FO 问题线性时间可解的条件。
有界扩张图类能刻画具有良好算法性质的稀疏图，且其上每个一阶逻辑可定义问题都可在线性时间内求解。然而，对有界扩张类做一阶解释或转导会产生更一般的稠密图类，它们似乎继承了许多此类算法性质。本文引入 lacon- 与 shrub-分解，并用它们刻画有界扩张类以及其他图类的一阶转导。核心结果是：如果能够高效计算有界扩张类转导的稀疏 shrub- 或 lacon-分解，那么在这些类上所有一阶逻辑可定义问题都可在线性时间内求解。该工作为稀疏图算法元定理向转导生成的稠密图类扩展提供了统一的结构性刻画。
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 work we introduce lacon- and shrub-decompositions and use them to characterize transductions of bounded expansion graph classes and other graph classes. If one can efficiently compute sparse shrub- or lacon-decompositions of transductions of bounded expansion classes then one can solve every problem definable in first-order logic in linear time on these classes.