Seymour's Second Neighborhood Conjecture for orientations of (pseudo)random graphs

Seymour's Second Neighborhood Conjecture (SNC) states that every oriented graph contains a vertex whose second neighborhood is as large its first neighborhood. We investigate the SNC for orientations of both binomial and pseudo random graphs, verifying asymptotically almost surely (a.a.s.) all G(n,p) if limsupn→∞p<1/4; uniformly-random orientation each weakly (p,Anp)-bijumbled order n density p, where p=Ω(n−1/2) 1−p=Ω(n−1/6) A>0 universal constant independent p. ε>0 p=p(n) with limsupn→∞p≤2/3−ε, minimum outdegree Ωε(n) satisfies SNC; p=p(n), SNC.