Let G = (V, E) be an undirected graph, with three numbers d0(e) ≥ d1(e) ≥ d2(e) ≥ 0 for each edge e ∈ E. A solution is a subset U ⊆ V and di(e) represents the cost contr...
We consider the concepts of a t-total vertex cover and a t-total edge cover (t 1), which generalize the notions of a vertex cover and an edge cover, respectively. A t-total verte...
We study the generalization of covering problems to partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard cov...
The Minimum Vertex Cover problem is the problem of, given a graph, finding a smallest set of vertices that touches all edges. We show that it is NP-hard to approximate this proble...
We study the partial vertex cover problem. Given a graph G = (V, E), a weight function w : V → R+ , and an integer s, our goal is to cover all but s edges, by picking a set of v...