4 citations · 10 across the 13 of their papers we have counts for
15 papers
Optimally building spanning graphs in semirandom graph processes
Michael Anastos, Maurício 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
Maurício 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
Maurício 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…
Long cycles in percolated expanders
Maurício Collares, Sahar Diskin, Joshua Erde +1
Given a graph and probability , we form the random subgraph by retaining each edge of independently with probability . Given and constants $0<c…
Universal behaviour of majority bootstrap percolation on high-dimensional geometric graphs
Maurício Collares, Joshua Erde, Anna Geisler +1
Majority bootstrap percolation is a monotone cellular automaton that can be thought of as a model of infection spreading in networks. Starting with an initially infected set, new v…
The evolution of the permutahedron
Maurício Collares, Joseph Doolittle, Joshua Erde
In their seminal paper introducing the theory of random graphs, Erdős and Rényi considered the evolution of the structure of a random subgraph of as the density increases fro…
The diameter of randomly twisted hypercubes
Lucas Aragão, Maurício 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…
A lower bound for set-colouring Ramsey numbers
Lucas Aragão, Maurício Collares, João Pedro Marciano +2
The set-colouring Ramsey number is defined to be the minimum such that if each edge of the complete graph is assigned a set of colours from $\{1,\ldots,r…
Counting orientations of random graphs with no directed k-cycles
Marcelo Campos, Maurício Collares, Guilherme Oliveira Mota
For every , we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of le…
The threshold for the constrained Ramsey property
Maurício Collares, Yoshiharu Kohayakawa, Carlos Gustavo Moreira +1
Given graphs , , and , let denote the property that in every edge colouring of there is a monochromatic copy of or a rain…
The Typical Structure of Sets with Small Sumset
Marcelo Campos, Maurício Collares, Robert Morris +2
In this paper we determine the number and typical structure of sets of integers with bounded doubling. In particular, improving recent results of Green and Morris, and of Mazur, we…
Counting restricted orientations of random graphs
Maurício Collares, Yoshiharu Kohayakawa, Robert Morris +1
We count orientations of avoiding certain classes of oriented graphs. In particular, we study , the number of orientations of the binomial random graph …
The typical structure of graphs with no large cliques
József Balogh, Neal Bushaw, Maurício Collares Neto +3
In 1987, Kolaitis, Prömel and Rothschild proved that, for every fixed , almost every -vertex -free graph is -partite. In this paper we extend this…
Maximum-size antichains in random set-systems
Maurício Collares Neto, Robert Morris
We show that, for , the largest set in a -random sub-family of the power set of containing no -chain has size $( k - 1 + o(1) ) p \binom{n}{…
The sharp threshold for maximum-size sum-free subsets in even-order abelian groups
Neal Bushaw, Maurício Collares Neto, Robert Morris +1
We study sum-free sets in sparse random subsets of even order abelian groups. In particular, we determine the sharp threshold for the following property: the largest such set is co…