The project aims to establish long-term scientific cooperation in Theoretical Computer Science between the Algorithms Research Group of the Department of Informatics of the University of Bergen (UiB) and the Algorithms, Graphs and Combinatorics (AlGCo) team of LIRMM (Laboratory of Computer Science, Robotics and Microelectronics of Montpellier). Within our project, we plan to attack hard computational problems on graphs in their most general form, combining the multivariate analysis with algorithmic meta-theorems and structural decompositions. Achieving the scientific objectives would demand a close collaboration of researchers of the AlGCo team of LIRMM and the Algorithms Research Group of UiB. The ALGCo team has a strong background in logic, algorithmic meta-theorems, and graph decompositions. The UiB part has a word-class leadership in all aspects of parameterized computation and other algorithmic techniques. Realizing the project's objective requires a combination of all these topics, which supports the complementarity of the two teams. Our main purpose is to extend the existing and initiate a new collaboration between the AlGCo team and the Algorithms Research Group. The proposal's key objective is to build a consortium for a project application within the Horizon Europe programme and to set up a LIA (Laboratoire International Associé).