Algorithmic Applications of Tree-Cut Width

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the treewidth minors. In this paper, we provide first algorithmic applications of hard combinatorial problems. Tree-cut is known be lower-bounded by function treewidth, but it can much larger and hence has potential facilitate efficient solution problems that are not fixed-parameter tractable (FPT) when parameterized treewidth. We introduce notion nice decompositions FPT algorithms for showcase Capacitated Vertex Cover, Dominating Set, Imbalance an input graph. On other hand, show List Coloring, Precoloring Extension, Boolean CSP (the last incidence graph) W[1]-hard unlikely width.