Unifying Theories for Graph Modification Problems

In this project, we explore the boundaries between tractability and intractability for graph modification problems. The study of such problems has developed fast in the past years with a wealth of new results being published. One common aspect of most such results is that they are tailored for very specific types of graph modification problems or specific types of inputs. The field lacks tools for unifying theories, such as algorithmic meta theorems, that can provide efficient algorithms for multiple types of modifications, or a wide range of inputs, at once. The goal of this project is to develop this missing theory.