@article{22157,
  abstract     = {A graph 𝐺 is said to be Ramsey for a tuple of graphs(𝐻 1 , … , 𝐻𝑟 ) if every 𝑟-coloring of the edges of 𝐺 con-tains a monochromatic copy of 𝐻𝑖 in color 𝑖, for some 𝑖.A fundamental question at the intersection of Ramseytheory and the theory of random graphs is to deter-mine the threshold at which the binomial randomgraph 𝐺𝑛,𝑝 becomes asymptotically almost surely Ram-sey for a fixed tuple (𝐻 1 , … , 𝐻𝑟 ), and a famous conjectureof Kohayakawa and Kreuter predicts this threshold.Earlier work of Mousset–Nenadov–Samotij, Bowtell–Hancock–Hyde, and Kuperwasser–Samotij–Wigdersonhas reduced this probabilistic problem to a determinis-tic graph decomposition conjecture. In this paper, weresolve this deterministic problem, thus proving theKohayakawa–Kreuter conjecture. Along the way, weprove a number of novel graph decomposition resultsthat may be of independent interest.},
  author       = {Christoph, Micha and Martinsson, Anders and Steiner, Raphael and Wigderson, Yuval},
  issn         = {1460-244X},
  journal      = {Proceedings of the London Mathematical Society},
  number       = {1},
  publisher    = {Wiley},
  title        = {{Resolution of the Kohayakawa–Kreuter conjecture}},
  doi          = {10.1112/plms.70013},
  volume       = {130},
  year         = {2025},
}

@article{22168,
  abstract     = {Let us say that a graph G is Ramsey for a tuple (H1, ... , Hr) of graphs if every r-colouring
of the edges of G contains a monochromatic copy of Hi in colour i, for some i ∈ [[r]].
A famous conjecture of Kohayakawa and Kreuter, extending seminal work of Rödl and
Rucinski, predicts the threshold at which the binomial random graph ´ Gn,p becomes Ramsey
for (H1, ... , Hr) asymptotically almost surely.
In this paper, we resolve the Kohayakawa–Kreuter conjecture for almost all tuples of
graphs. Moreover, we reduce its validity to the truth of a certain deterministic statement,
which is a clear necessary condition for the conjecture to hold. All of our results actually hold in greater generality, when one replaces the graphs H1, ... , Hr by finite families
H1, ... , Hr. Additionally, we pose a natural (deterministic) graph-partitioning conjecture,
which we believe to be of independent interest, and whose resolution would imply the
Kohayakawa–Kreuter conjecture.},
  author       = {KUPERWASSER, EDEN and SAMOTIJ, WOJCIECH and Wigderson, Yuval},
  issn         = {1469-8064},
  journal      = {Mathematical Proceedings of the Cambridge Philosophical Society},
  number       = {3},
  pages        = {293--320},
  publisher    = {Cambridge University Press},
  title        = {{On the Kohayakawa–Kreuter conjecture}},
  doi          = {10.1017/s0305004125000143},
  volume       = {178},
  year         = {2025},
}