From the 1 of 9 linked papers with an AI index.
9 papers
A short proof of a central limit theorem for the order of the giant component and -core
Michael Anastos, Joshua Erde, Mihyun Kang +1
The paper introduces a simple approach based on the Efron–Stein inequality to prove central limit theorems for the size of the giant component and the k‑core in sparse random graph…
Matchings in the hypercube with specified edges
Joshua Erde
Given a matching in the hypercube , the \emph{profile} of is the vector such that contains edges whose en…
The evolution of the permutahedron
MaurÃcio Collares, Joseph Doolittle, Joshua Erde
In their seminal paper introducing the theory of random graphs, ErdÅs and Rényi considered the evolution of the structure of a random subgraph of as the density increases f…
Optimally building spanning graphs in semirandom graph processes
Michael Anastos, MaurÃcio Collares, Joshua Erde +3
The semirandom graph process constructs a graph in a series of rounds, starting with the empty graph on vertices. In each round, a player is offered a vertex chosen uni…
Majority bootstrap percolation on the permutahedron and other high-dimensional graphs
MaurÃcio Collares, Joshua Erde, Anna Geisler +1
Majority bootstrap percolation is a model of infection spreading in networks. Starting with a set of initially infected vertices, new vertices become infected once half of their ne…
Cycle lengths in the percolated hypercube
Michael Anastos, Sahar Diskin, Joshua Erde +3
Let be the random subgraph of the -dimensional binary hypercube obtained after edge-percolation with probability . It was shown recently by the authors that, for ever…