A dominating set D of a graph G = (V, E) is a subset of vertices such that every vertex in V \ D has at least one neighbour in D. Moreover if D is an independent set, i.e. no verti...
In this paper we introduce a general strategy for approximating the solution to minimisation problems in random regular graphs. We describe how the approach can be applied to the m...
We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that...
We study various optimization problems in t-subtree graphs, the intersection graphs of tsubtrees, where a t-subtree is the union of t disjoint subtrees of some tree. This graph cl...
We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded gr...