We study the cover time of multiple random walks. Given a graph G of n vertices, assume that k independent random walks start from the same vertex. The parameter of interest is the...
We give tight bounds on the parallel complexity of some problems involving random graphs. Speci cally, we show that a Hamiltonian cycle, a breadth rst spanning tree, and a maximal...
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 ...
We consider the parametric minimum spanning tree problem, in which we are given a graph with edge weights that are linear functions of a parameter and wish to compute the sequenc...
Pankaj K. Agarwal, David Eppstein, Leonidas J. Gui...
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...