Towards the Kohayakawa--Kreuter conjecture on asymmetric Ramsey properties

Abstract

For fixed graphs $F_1,\dots ,F_r$, we prove an upper bound on the threshold function for the property that $G(n,p)\to (F_1,\dots ,F_r)$. This establishes the $1$-statement of a conjecture of Kohayakawa and Kreuter.

12 pages; several minor changes