We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
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 ...
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...
Given a connected, weighted, undirected graph G and a bound D, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path betw...
Abstract. We show that a maximum cut of a random graph below the giantcomponent threshold can be found in linear space and linear expected time by a simple algorithm. In fact, the ...