@article{19503,
  abstract     = {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.},
  author       = {Christoph, Micha and Petrova, Kalina H and Steiner, Raphael},
  issn         = {1469-2163},
  journal      = {Combinatorics Probability and Computing},
  number       = {4},
  pages        = {559--564},
  publisher    = {Cambridge University Press},
  title        = {{A note on digraph splitting}},
  doi          = {10.1017/S0963548325000045},
  volume       = {34},
  year         = {2025},
}