We study the problem of local search on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a v...
We prove that the out-distance sequence {f+ (k)} of a vertex-transitive digraph of finite or infinite degree satisfies f+ (k + 1) f+ (k)2 for k 1, where f+ (k) denotes the numbe...
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...