1 citations · 2 across the 7 of their papers we have counts for
7 papers
Ramsey properties for tilings in random graphs
Lucas Aragão, Xinbu Cheng, Rafael Filipe +3
Let be the graph formed by vertex-disjoint copies of a graph . Let denote that, in any -colouring of the edges of , there exists a monochromatic cop…
An exponential upper bound for induced Ramsey numbers
Lucas Aragão, Marcelo Campos, Gabriel Dahia +2
The induced Ramsey number of a graph is the minimum number such that there exists a graph with vertices for which all -colourings of its edg…
Degree conditions for Ramsey goodness of paths
Lucas Aragão, João Pedro Marciano, Walner Mendonça
A classical result of Chvátal implies that if , then any colouring of the edges of in red and blue contains either a monochromatic red or a monoch…
On the number of monochromatic solutions to multiplicative equations
Lucas Aragão, Jonathan Chapman, Miquel Ortega +1
The following question was asked by Prendiville: given an -colouring of the interval , what is the minimum number of monochromatic solutions of the equation $x…
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…
Localised graph Maclaurin inequalities
Lucas Aragão, Victor Souza
The Maclaurin inequalities for graphs are a broad generalisation of the classical theorems of Turán and Zykov. In a nutshell they provide an asymptotically sharp answer to the foll…
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…