article published yes Patryk Morawski author Kalina H Petrova author 554ff4e4-f325-11ee-b0c4-a10dbd523381 MaKw department IST-BRIDGE: International postdoctoral program project 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. https://research-explorer.ista.ac.at/download/21884/21893/2026_ElectrJournCombinatorics_Morawski.pdf application/pdfno https://creativecommons.org/licenses/by-nd/4.0/ Electronic Journal of Combinatorics2026 eng 1077-8926 2306.1464810.37236/13316 332 P. Morawski, K.H. Petrova, Electronic Journal of Combinatorics 33 (2026). Morawski P, Petrova KH. 2026. Randomly perturbed digraphs also have bounded-degree spanning trees. Electronic Journal of Combinatorics. 33(2), P2.24. 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> Morawski, Patryk, and Kalina H. Petrova. “Randomly Perturbed Digraphs Also Have Bounded-Degree Spanning Trees.” <i>Electronic Journal of Combinatorics</i>, vol. 33, no. 2, P2.24, Electronic Journal of Combinatorics, 2026, doi:<a href="https://doi.org/10.37236/13316">10.37236/13316</a>. Morawski, Patryk, and Kalina H Petrova. “Randomly Perturbed Digraphs Also Have Bounded-Degree Spanning Trees.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2026. <a href="https://doi.org/10.37236/13316">https://doi.org/10.37236/13316</a>. P. Morawski and K. H. Petrova, “Randomly perturbed digraphs also have bounded-degree spanning trees,” <i>Electronic Journal of Combinatorics</i>, vol. 33, no. 2. Electronic Journal of Combinatorics, 2026. Morawski, P., &#38; Petrova, K. H. (2026). Randomly perturbed digraphs also have bounded-degree spanning trees. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/13316">https://doi.org/10.37236/13316</a> 218842026-05-17T22:02:11Z2026-05-18T08:50:18Z