On the Kohayakawa–Kreuter conjecture KUPERWASSER, EDEN SAMOTIJ, WOJCIECH Wigderson, Yuval 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. Cambridge University Press 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/22168 KUPERWASSER E, SAMOTIJ W, Wigderson Y. On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2025;178(3):293-320. doi:<a href="https://doi.org/10.1017/s0305004125000143">10.1017/s0305004125000143</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/s0305004125000143 info:eu-repo/semantics/altIdentifier/issn/0305-0041 info:eu-repo/semantics/altIdentifier/e-issn/1469-8064 info:eu-repo/semantics/altIdentifier/arxiv/2307.16611 info:eu-repo/semantics/openAccess