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...
Suppose that we are given a set of n elements d of which are “defective”. A group test can check for any subset, called a pool, whether it contains a defective. It is well know...
A graph G homogeneously embeds in a graph H if for every vertex x of G and every vertex y of H there is an induced copy of G in H with x at y. The graph G uniformly embeds in H if...
The class of graphs where the size of a minimum vertex cover equals that of a maximum matching is known as K¨onig-Egerv´ary graphs. K¨onig-Egerv´ary graphs have been studied ex...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...