P. Araújo

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20232026

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math.CO2026

Semidegree threshold for spanning trees in oriented graphs

Pedro Araújo, Giovanne Santos, Maya Stein

We show that for all $γ > 0$ and $Δ \in N$ , there is some $n_{0}$ such that, if $n \geq n_{0}$ , then every oriented graph on $n$ vertices with minimum semidegree at least $(3/8…

math.CO2023

Local central limit theorem for triangle counts in sparse random graphs

Pedro Araújo, Letícia 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 $H$ …