article published yes Micha Christoph author Anders Martinsson author Raphael Steiner author Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 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. https://creativecommons.org/licenses/by/4.0/ Wiley2025 eng 0024-6115 1460-244X 2402.0304510.1112/plms.70013 1301 yes Christoph, Micha, Anders Martinsson, Raphael Steiner, and Yuval Wigderson. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href="https://doi.org/10.1112/plms.70013">https://doi.org/10.1112/plms.70013</a>. M. Christoph, A. Martinsson, R. Steiner, Y. Wigderson, Proceedings of the London Mathematical Society 130 (2025). Christoph, Micha, et al. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1, e70013, Wiley, 2025, doi:<a href="https://doi.org/10.1112/plms.70013">10.1112/plms.70013</a>. M. Christoph, A. Martinsson, R. Steiner, and Y. Wigderson, “Resolution of the Kohayakawa–Kreuter conjecture,” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1. Wiley, 2025. Christoph, M., Martinsson, A., Steiner, R., &#38; Wigderson, Y. (2025). Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href="https://doi.org/10.1112/plms.70013">https://doi.org/10.1112/plms.70013</a> Christoph M, Martinsson A, Steiner R, Wigderson Y. Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. 2025;130(1). doi:<a href="https://doi.org/10.1112/plms.70013">10.1112/plms.70013</a> Christoph M, Martinsson A, Steiner R, Wigderson Y. 2025. Resolution of the Kohayakawa–Kreuter conjecture. Proceedings of the London Mathematical Society. 130(1), e70013. 221572026-06-29T10:50:35Z2026-07-08T10:24:21Z