5 papers
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…
Counting independent sets in expanding bipartite regular graphs
MaurÃcio Collares, Joshua Erde, Anna Geisler +1
In this paper we provide an asymptotic expansion for the number of independent sets in a general class of regular, bipartite graphs satisfying some vertex-expansion properties, ext…
The diameter of randomly twisted hypercubes
Lucas Aragão, MaurÃcio Collares, Gabriel Dahia +1
The -dimensional random twisted hypercube is constructed recursively by taking two instances of , with any joint distribution, and adding a rand…