Parameterized complexity of graph problems with matroid constraints

Abstract

This report delves into the parameterized complexity of classical graph problems under matroid constraints. By exploring Independent Stable Set and various vertex-cut problems, we develop efficient algorithms leveraging advanced techniques such as flow augmentation and representative families. The focus is on algorithmic insights for Independent Stable Set in d-degenerate graphs, as well as matroidal extensions of (s, t)-cut. These results provide a deeper understanding of the interplay between graph theory and matroid theory.