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- W4384306212 abstract "Seymour's Second Neighborhood Conjecture (SNC) states that every oriented graph contains a vertex whose second neighborhood is as large as its first neighborhood. We investigate the SNC for orientations of both binomial and pseudo random graphs, verifying the SNC asymptotically almost surely (a.a.s.) for all orientations of G(n,p) if limsupn→∞p<1/4; and for a uniformly-random orientation of each weakly (p,Anp)-bijumbled graph of order n and density p, where p=Ω(n−1/2) and 1−p=Ω(n−1/6) and A>0 is a universal constant independent of both n and p. for all ε>0 and p=p(n) with limsupn→∞p≤2/3−ε, every orientation of G(n,p) with minimum outdegree Ωε(n) satisfies the SNC; and for all p=p(n), a random orientation of G(n,p) satisfies the SNC." @default.
- W4384306212 created "2023-07-15" @default.
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- W4384306212 date "2023-12-01" @default.
- W4384306212 modified "2023-10-17" @default.
- W4384306212 title "Seymour's Second Neighborhood Conjecture for orientations of (pseudo)random graphs" @default.
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- W4384306212 doi "https://doi.org/10.1016/j.disc.2023.113583" @default.
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