Igor Araujo

activity

20202023

collaborators

9 papers

math.CO2023

Tiling edge-ordered graphs with monotone paths and other structures

Igor Araujo, Simón Piga, Andrew Treglown +1

Given graphs $F$ and $G$ , a perfect $F$ -tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$ that together cover all the vertices in $G$ . The study of the minimum…

math.CO2023

Triangle Percolation on the Grid

Igor Araujo, Bryce Frederickson, Robert A. Krueger +5

We consider a geometric percolation process partially motivated by recent work of Hejda and Kala. Specifically, we start with an initial set $X \subseteq Z^{2}$ , and then it…

math.CO2023

Realizable Standard Young Tableaux

Igor Araujo, Alexander E. Black, Amanda Burcroff +3

Given two vectors $u$ and $v$ , their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$ . If the entries of $u$ and $v$ are increasing and sufficiently gener…

math.CO2022

On oriented cycles in randomly perturbed digraphs

Igor Araujo, József Balogh, Robert A. Krueger +2

In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $α > 0$ , there exists a constant $C$ such…

math.CO2022

Rainbow Connection for Complete Multipartite Graphs

Igor Araujo, Kareem Benaissa, Richard Bi +3

A path in an edge-colored graph is said to be rainbow if no color repeats on it. An edge-colored graph is said to be rainbow $k$ -connected if every pair of vertices is connected by…

math.CO2022

New Lower Bounds For Essential Covers Of The Cube

Igor Araujo, József Balogh, Letícia Mattos

An essential cover of the vertices of the $n$ -cube ${0, 1}^{n}$ by hyperplanes is a minimal covering where no hyperplane is redundant and every variable appears in the equation of a…

math.CO2022

On the Maximum $F_{5}$ -free Subhypergraphs of a Random Hypergraph

Igor Araujo, József Balogh, Haoran Luo

Denote by $F_{5}$ the $3$ -uniform hypergraph on vertex set ${1, 2, 3, 4, 5}$ with hyperedges ${123, 124, 345}$ . Balogh, Butterfield, Hu, and Lenz proved that if $p > K lo g n / n$ for…

math.CO2021

On the number of sum-free triplets of sets

Igor Araujo, József Balogh, Ramon I. Garcia

We count the ordered sum-free triplets of subsets in the group $Z / p Z$ , i.e., the triplets $(A, B, C)$ of sets $A, B, C \subset Z / p Z$ for which the e…

math.CO2020

Maximum determinant and permanent of sparse 0-1 matrices

Igor Araujo, József Balogh, Yuzhou Wang

We prove that the maximum determinant of an $n \times n$ matrix, with entries in ${0, 1}$ and at most $n + k$ non-zero entries, is at most $2^{k /3}$ , which is best possible when $k…

Tiling edge-ordered graphs with monotone paths and other structures

Triangle Percolation on the Grid

Realizable Standard Young Tableaux

On oriented cycles in randomly perturbed digraphs

Rainbow Connection for Complete Multipartite Graphs

New Lower Bounds For Essential Covers Of The Cube

On the Maximum F5​-free Subhypergraphs of a Random Hypergraph

On the number of sum-free triplets of sets

Maximum determinant and permanent of sparse 0-1 matrices

On the Maximum $F_{5}$ -free Subhypergraphs of a Random Hypergraph