In this paper, we investigate algorithms for some related graph parameters. Each of these asks for a linear ordering of the vertices of the graph (or can be formulated as such), and there are constructive linear time ...

Graph minors theory, developed by Robertson & Seymour, provides a list of powerful theoretical results and tools. However, the wide spread opinion in Graph Algorithms community about this theory is that it is mainly of ...

We present a fixed parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of the K_{5} or K_3,3 as a minor in time O(3^{6sqrt{34 k}}n^{O(1)}). In fact, we present our ...

Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function ...

The (k,r)-center problem} asks whether an input graph G has atr most k vertices (called centers) such that every vertex of $ is within distance at most r from some center. In this paper we prove that the (k,r)-center ...

In general, graph search can be described in terms of a sequence of searchers' moves on a graph, able to capture a fugitive resorting on its vertices/edges. Several variations of graph search have been introduced, ...

We extend the well-studied concept of a graph power to that of a k-leaf power G of a tree T: G is formed by creating a node for each leaf in the tree and an edge between a pair of nodes if and only if the associated ...

Submodular functions have appeared to be a key tool for proving the monotonicity of several graph searching games. In this paper we provide a general game theoretic framework able to unify old and new monotonicity ...

We demonstrate a kernel of size O(k^2) for 3-HITTING SET when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k^3) ...