Igor Araujo

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4 papers · 1 filter

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.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…