We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n, p) in the critical window, that is, for p = n−1 + λn−4/...
Laman’s characterization of minimally rigid 2-dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and expl...
Bill Jackson, Brigitte Servatius, Herman Servatius
In this paper we consider 3-dimensional generic bar-and-joint realizations of squares of graphs. These graphs are also called molecular graphs due to their importance in the study...
We consider random walks on two classes of random graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices. Let (t) be the subgraph induced by ...