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...
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let Gn,p denote a random graph on n vertices with edge probab...
We prove the following inequality: for every positive integer n and every collection X1, . . . , Xn of nonnegative independent random variables that each has expectation 1, the pr...
We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relati...
A Random Geometric Graph (RGG) in two dimensions is constructed by distributing n nodes independently and uniformly at random in [0, n ]2 and creating edges between every pair of...
Milan Bradonji, Robert Elsässer, Tobias Friedrich...