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...
The rigidity of squares of graphs in three-space has important applications to the study of flexibility in molecules. The Molecular Conjecture, posed in 1984 by T-S. Tay and W. Wh...
: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures...
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/...