João Pedro Marciano

activity

20232026

most cited

C_{10}

has positive Turán density in the hypercube

1 citations · 3 across the 10 of their papers we have counts for

collaborators

10 papers

math.CO2026

Counting sets with given doubling via dimension

Marcelo Campos, Gabriel Dahia, João Pedro Marciano

We determine, up to a factor of $2^{o (k)}$ , the number of $k$ -sets $A \subset {1, \dots, n}$ such that $∣ A + A ∣ \leq m$ , where $k = Θ (lo g n)$ and $m \leq k^{1 + α}$ , for small…

math.CO2026

Dense sets without large sumsets

Gabriel Dahia, João Pedro Marciano, Victor Souza

We prove, for all fixed $0 < δ < 1$ , and all sufficiently large $n$ , that there exists $S \subset [n]$ with $∣ S ∣ \geq δ n$ such that $A + B \neq \subset S$ for all ${A, B \subset \mat…

math.CO2025

An exponential upper bound for induced Ramsey numbers

Lucas Aragão, Marcelo Campos, Gabriel Dahia +2

The induced Ramsey number $R_{ind} (H; r)$ of a graph $H$ is the minimum number $N$ such that there exists a graph with $N$ vertices for which all $r$ -colourings of its edg…

math.CO2024

Colour-bias perfect matchings in hypergraphs

Hiêp Hàn, Richard Lang, João Pedro Marciano +4

We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main r…

math.CO2024

On the independence number of sparser random Cayley graphs

Marcelo Campos, Gabriel Dahia, João Pedro Marciano

The Cayley sum graph $Γ_{A}$ of a set $A \subseteq Z_{n}$ is defined to have vertex set $Z_{n}$ and an edge between two distinct vertices $x, y \in Z_{n}$ if $x…

math.CO2024

Degree conditions for Ramsey goodness of paths

Lucas Aragão, João Pedro Marciano, Walner Mendonça

A classical result of Chvátal implies that if $n \geq (r - 1) (t - 1) + 1$ , then any colouring of the edges of $K_{n}$ in red and blue contains either a monochromatic red $K_{r}$ or a monoch…

math.CO2024★ 1 cited

$C_{10}$ has positive Turán density in the hypercube

Alexandr Grebennikov, João Pedro Marciano

The $n$ -dimensional hypercube $Q_{n}$ is a graph with vertex set ${0, 1}^{n}$ such that there is an edge between two vertices if and only if they differ in exactly one coordinate. For…

math.CO2023★ 1 cited

The diameter of randomly twisted hypercubes

Lucas Aragão, Maurício Collares, Gabriel Dahia +1

The $n$ -dimensional random twisted hypercube $G_{n}$ is constructed recursively by taking two instances of $G_{n - 1}$ , with any joint distribution, and adding a rand…

cs.CC2023

The complexity of decomposing a graph into a matching and a bounded linear forest

Agnijo Banerjee, João Pedro Marciano, Adva Mond +2

Deciding whether a graph can be edge-decomposed into a matching and a $k$ -bounded linear forest was recently shown by Campbell, H{ö}rsch and Moore to be NP-complete for every $k \g…

math.CO2023★ 1 cited

A lower bound for set-colouring Ramsey numbers

Lucas Aragão, Maurício Collares, João Pedro Marciano +2

The set-colouring Ramsey number $R_{r, s} (k)$ is defined to be the minimum $n$ such that if each edge of the complete graph $K_{n}$ is assigned a set of $s$ colours from $\{1,\ldots,r…

Counting sets with given doubling via dimension

Dense sets without large sumsets

An exponential upper bound for induced Ramsey numbers

Colour-bias perfect matchings in hypergraphs

On the independence number of sparser random Cayley graphs

Degree conditions for Ramsey goodness of paths

C10​ has positive Turán density in the hypercube

The diameter of randomly twisted hypercubes

The complexity of decomposing a graph into a matching and a bounded linear forest

A lower bound for set-colouring Ramsey numbers

$C_{10}$ has positive Turán density in the hypercube