For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph...
A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no k-Dominating Set, or (2) produces a do...
Rodney G. Downey, Michael R. Fellows, Catherine Mc...
We give the first linear kernels for DOMINATING SET and CONNECTED DOMINATING SET problems on graphs excluding a fixed graph H as a minor. In other words, we give polynomial time...
Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, ...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
A graph is distance-hereditary if and only if each cycle on five or more vertices has at least two crossing chords. We present linear time algorithms for the minimum r-dominating c...