For　graphs　G　and　H,　let　signify　that　any　red/blue　edge　coloring　of　G　contains　a　monochromatic　H　as　a　subgraph.　Denote　.　For　any　and　n,　we　say　that　G　is　partition　universal　for　if　for　every　.　Let　be　the　random　spanning　subgraph　of　the　complete　r-partite　graph　with　N　vertices　in　each　part,　in　which　each　edge　of　appears　with　probability　p　independently　and　randomly.　We　prove　that　for　fixed　there　exist　constants　r,　B　and　C　depending　only　on　such　that　if　and　,　then　asymptotically　almost　surely　is　partition　universal　for　H(Delta,　n).