Conclusion and open problems
We will leave it to the researchers of the next ten years and beyond to decide which of the results presented in this book are the most important. Here we will only indicate what are, in our opinion, the main open problems and research directions, among those that are closely related with the topics of this book.
This topic, studied in Chapter 6, is the most difficult to discuss because of the large number of new articles published every year. Hence, the following comments have a good chance of becoming rapidly obsolete.
The algorithmic consequences of the Recognizability Theorem depend crucially on algorithms that construct graph decompositions of the relevant types or, equivalently, that ...