Leticia Mattos

collaborators

6 papers

math.CO2025

On the Prague dimension of sparse random graphs

Felix Joos, LetÃcia Mattos

The Prague dimension of a graph $G$ is defined as the minimum number of complete graphs whose direct product contains $G$ as an induced subgraph. Introduced in the 1970s by NeÅ¡etÅ…

math.CO2025

Clique packings in random graphs

Simon Griffiths, LetÃcia Mattos

We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense ErdÅs-RÃ©nyi random graph $G (n, p)$ . Recently Acan and Kahn showed that the larges…

math.CO2025

Local central limit theorem for triangle counts in sparse random graphs

Pedro AraÃºjo, LetÃcia Mattos

Let $X_{H}$ be the number of copies of a fixed graph $H$ in $G (n, p)$ . In 2016, Gilmer and Kopparty conjectured that a local central limit theorem should hold for $X_{H}$ as long as $H$ …

math.CO2025

On the number of sets with small sumset

Dingyuan Liu, LetÃcia Mattos, Tibor SzabÃ³

We investigate subsets with small sumset in arbitrary abelian groups. For an abelian group $G$ and an $n$ -element subset $Y \subseteq G$ we show that if $m ≪ s^{2} / (lo g n)^{2}$ , the…

math.CO2025

On almost Gallai colourings in complete graphs

Alexandr Grebennikov, LetÃcia Mattos, Tibor SzabÃ³

For $t \in N$ , we say that a colouring of $E (K_{n})$ is $almost$ $t$ - $Gallai$ if no two rainbow $t$ -cliques share an edge. Motivated by a lemma of Berkowit…

math.CO2025

On product Schur triples in the integers

LetÃcia Mattos, Domenico Mergoni Cecchelli, Olaf Parczyk

Schur's theorem states that in any $k$ -colouring of the set of integers $[n]$ there is a monochromatic solution to $a + b = c$ , provided $n$ is sufficiently large. Abbott and Wang stud…