ABSTRACT: Let G(n, c/n) and Gr(n) be an n-node sparse random graph and a sparse random rregular graph, respectively, and let I(n, r) and I(n, c) be the sizes of the largest indepen...
An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exis...
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
The standard paradigm for online power of two choices problems in random graphs is the Achlioptas process. Here we consider the following natural generalization: Starting with G0 a...
Let G = (V, E) be an undirected loopless graph with possible parallel edges and s, t V . Assume that s is labelled at the initial time step and that every labelled vertex copies i...