article published yes Micha Christoph author Kalina H Petrova author 554ff4e4-f325-11ee-b0c4-a10dbd523381 Raphael Steiner author MaKw department IST-BRIDGE: International postdoctoral program project 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. https://research-explorer.ista.ac.at/download/19503/20135/2025_CombProbComputing_Christoph.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Cambridge University Press2025 eng 0963-5483 1469-2163 2310.08449 00144924570000110.1017/S0963548325000045 344559-564 Christoph M, Petrova KH, Steiner R. 2025. A note on digraph splitting. Combinatorics Probability and Computing. 34(4), 559–564. Christoph, Micha, et al. “A Note on Digraph Splitting.” <i>Combinatorics Probability and Computing</i>, vol. 34, no. 4, Cambridge University Press, 2025, pp. 559–64, doi:<a href="https://doi.org/10.1017/S0963548325000045">10.1017/S0963548325000045</a>. M. Christoph, K. H. Petrova, and R. Steiner, “A note on digraph splitting,” <i>Combinatorics Probability and Computing</i>, vol. 34, no. 4. Cambridge University Press, pp. 559–564, 2025. Christoph, Micha, Kalina H Petrova, and Raphael Steiner. “A Note on Digraph Splitting.” <i>Combinatorics Probability and Computing</i>. Cambridge University Press, 2025. <a href="https://doi.org/10.1017/S0963548325000045">https://doi.org/10.1017/S0963548325000045</a>. M. Christoph, K.H. Petrova, R. Steiner, Combinatorics Probability and Computing 34 (2025) 559–564. 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> Christoph, M., Petrova, K. H., &#38; Steiner, R. (2025). A note on digraph splitting. <i>Combinatorics Probability and Computing</i>. Cambridge University Press. <a href="https://doi.org/10.1017/S0963548325000045">https://doi.org/10.1017/S0963548325000045</a> 195032025-04-06T22:01:32Z2025-09-30T11:26:00Z