Abstract The main focus of this thesis is on using the divide and conquer technique toeciently solve graph problems that are in general intractable. We work inthe eld of parameterized algorithms,… Expand

We look at dynamic programming algorithms for propositional model counting, also called #SAT, and MaxSAT using similar, but more modern, graph structure tools.Expand

With respect to a hereditary class C of graphs, a k -chromatic graph G ? C is said to be k -critical if every proper subgraph of G belonging to C is k - 1 colorable. It is known that there is a… Expand

Boolean-width is a recently introduced graph invariant. Similar to tree-width, it measures the structural complexity of graphs. Given any graph G and a decomposition of G of boolean-width k, we give… Expand

We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods-Boolean sums of neighborhoods–across a cut of a graph.Expand