We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree . We prove that, for every > 0, the d...
Martin E. Dyer, Alan M. Frieze, Thomas P. Hayes, E...
We examine the relationship of a graph G and its random subgraphs which are defined by independently choosing each edge with probability p. Suppose that G has a spectral gap λ (...
We study the cover time of a random walk on the largest component of the random graph Gn,p. We determine its value up to a factor 1 + o(1) whenever np = c > 1, c = O(ln n). In ...
We consider the performance of a simple greedy matching algorithm MINGREEDY when applied to random cubic graphs. We show that if λn is the expected number of vertices not matched...
A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn Rd at random (i.i.d. according to some probability distribution with a bounded density function) and...