Randomly perturbed digraphs also have bounded-degree spanning trees Morawski, Patryk Petrova, Kalina H ddc:510 We show that a randomly perturbed digraph, where we start with a dense digraph Dα and add a small number of random edges to it, will typically contain a fixed orientation of a bounded-degree spanning tree. This answers a question posed by Araujo, Balogh, Krueger, Piga and Treglown and generalizes the corresponding result for randomly perturbed graphs by Krivelevich, Kwan and Sudakov. More specifically, we prove that there exists a constant c=c(α,Δ) such that if T is an oriented tree with maximum degree Δ and Dα is an n-vertex digraph with minimum semidegree αn, then the graph obtained by adding cn uniformly random edges to Dα will contain T with high probability. Electronic Journal of Combinatorics 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/21884 https://research-explorer.ista.ac.at/download/21884/21893 Morawski P, Petrova KH. Randomly perturbed digraphs also have bounded-degree spanning trees. <i>Electronic Journal of Combinatorics</i>. 2026;33(2). doi:<a href="https://doi.org/10.37236/13316">10.37236/13316</a> eng info:eu-repo/semantics/altIdentifier/doi/10.37236/13316 info:eu-repo/semantics/altIdentifier/e-issn/1077-8926 info:eu-repo/semantics/altIdentifier/arxiv/2306.14648 info:eu-repo/semantics/openAccess