Spanners of bounded degree graphs

Is there some function f : N → N and an algorithm that given a graph G and an integer k, either decides that mimw(G) > k, or outputs a branch decomposition of G of mim-width at

Maximum Induced Forest and Maximum Induced Tree are W[1]-hard pa- rameterized by k + w, and Feedback Vertex Set is W[1]-hard parameterized by w, where k denotes the solution size and

In the Terrain Guarding problem, the input is a terrain and a positive integer k, and the task is to decide whether one can place guards on at most k points on a given terrain such

We also present refinements of our bounds for other graph classes such as K r -minor free graphs and graphs of bounded genus.. © 2010

Let Γ k (k 2) be the graph obtained from the ( k × k ) -grid by triangulating internal faces of the ( k × k ) -grid such that all internal vertices become of degree 6, all

In particular, we show that for all positive integers t and W , the Minimum Weight t -spanner problem admits a EPTAS on apex-minor-free graphs with positive integer weights of edges

We show that for several classes of sparse graphs, including planar graphs, graphs of bounded vertex degree and graphs excluding some fixed graph as a minor, an improved solution in

Observe that this algorithm also works on graphs of bounded local treewidth, because if the graph has a vertex at distance more than k from the root, then any strategy that protects