@article{21884,
  abstract     = {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.},
  author       = {Morawski, Patryk and Petrova, Kalina H},
  issn         = {1077-8926},
  journal      = {Electronic Journal of Combinatorics},
  number       = {2},
  publisher    = {Electronic Journal of Combinatorics},
  title        = {{Randomly perturbed digraphs also have bounded-degree spanning trees}},
  doi          = {10.37236/13316},
  volume       = {33},
  year         = {2026},
}