Target Set Selection in Dense Graph Classes

In this paper, we study the Target Set Selection problem from a parameterized complexity perspective. Here for given graph and threshold each vertex, task is to find set of vertices (called target set) that activates whole during following iterative process. A vertex outside active becomes if number so far activated in its neighborhood at least threshold. We give two algorithms special case where has half neighbors (the so-called Majority problem) parameterizations by diversity twin cover input graph. complement these results negative side. hardness proof when (a restriction of) modular-width---a natural generalization both previous structural parameters. also show or \sf W[1]-hard there no on thresholds.