We are interested in characterizing which classes of finite graphs are well-quasi-ordered by the induced subgraph relation. To that end, we devise an algorithm to decide whether a class of finite graphs well-quasi-ordered by the induced subgraph relation when the vertices are labelled using a finite set. In this process, we answer positively to a conjecture of Pouzet, under the extra assumption that the class is of bounded linear clique-width. As a byproduct of our approach, we obtain a new proof of an earlier result from Daliagault, Rao, and Thomass\'e, by uncovering a connection between well-quasi-orderings on graphs and the gap embedding relation of Dershowitz and Tzameret.

翻译：我们致力于刻画有限图类中哪些类在诱导子图关系下是良拟序的。为此，我们设计了一种算法，用于判定当顶点使用有限集进行标记时，一个有限图类在诱导子图关系下是否为良拟序的。在此过程中，我们在额外假设该类具有有界线性团宽度的条件下，对Pouzet的一个猜想给出了肯定的回答。作为我们方法的副产品，通过揭示图上的良拟序与Dershowitz和Tzameret的间隙嵌入关系之间的联系，我们获得了Daliagault、Rao和Thomassé早期结果的一个新证明。