Connections in Randomly Oriented Graphs


Given an undirected graph G, let us randomly orient G by tossing independent (possibly biased) coins, one for each edge of G. Writing a→ b for the event that there exists a directed path from a vertex a to a vertex b in such a random orientation, we prove that for any three vertices s, a and b of G, we have P(s→ a ∩ s→ b) ≥ P(s→ a)P(s→ b). 


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