Resolution of the Kohayakawa–Kreuter conjecture Christoph, Micha Martinsson, Anders Steiner, Raphael Wigderson, Yuval ddc:500 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. Wiley 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/22157 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/plms.70013 info:eu-repo/semantics/altIdentifier/issn/0024-6115 info:eu-repo/semantics/altIdentifier/e-issn/1460-244X info:eu-repo/semantics/altIdentifier/arxiv/2402.03045 info:eu-repo/semantics/openAccess