João Pedro Marciano

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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

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9 papers · 1 filter

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…