A note on digraph splitting Christoph, Micha Petrova, Kalina H Steiner, Raphael ddc:510 A tantalizing open problem, posed independently by Stiebitz in 1995 and by Alon in 1996 and again in 2006, asks whether for every pair of integers s,t≥1 there exists a finite number F(s,t) such that the vertex set of every digraph of minimum out-degree at least F(s,t) can be partitioned into non-empty parts A and B such that the subdigraphs induced on A and B have minimum out-degree at least s and t , respectively. In this short note, we prove that if F(2,2) exists, then all the numbers F(s,t) with s,t≥1 exist and satisfy F(s,t)=Θ(s+t) . In consequence, the problem of Alon and Stiebitz reduces to the case s=t=2 . Moreover, the numbers F(s,t) with s,t≥2 either all exist and grow linearly, or all of them do not exist. Cambridge University Press 2025 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/19503 https://research-explorer.ista.ac.at/download/19503/20135 Christoph M, Petrova KH, Steiner R. A note on digraph splitting. <i>Combinatorics Probability and Computing</i>. 2025;34(4):559-564. doi:<a href="https://doi.org/10.1017/S0963548325000045">10.1017/S0963548325000045</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/S0963548325000045 info:eu-repo/semantics/altIdentifier/issn/0963-5483 info:eu-repo/semantics/altIdentifier/e-issn/1469-2163 info:eu-repo/semantics/altIdentifier/wos/001449245700001 info:eu-repo/semantics/altIdentifier/arxiv/2310.08449 info:eu-repo/semantics/openAccess