Using the concept of discrete noiseless channels, it was shown by Shannon in A Mathematical Theory of Communication that the ultimate performance of an encoder for a constrained sy...
Let G(3n, p, 3) be a random 3-colorable graph on a set of 3n vertices generated as follows. First, split the vertices arbitrarily into three equal color classes and then choose ev...
We study a dynamically evolving random graph which adds vertices and edges using preferential attachment and is “attacked by an adversary”. At time t, we add a new vertex xt a...
We present an algorithm to compute the cycle structure of large directed graphs where each node has exactly one outgoing edge. Such graphs appear as state diagrams of finite stat...
In this paper we consider three models for random graphs that utilize the inner product as their fundamental object. We analyze the behavior of these models with respect to cluster...