For two-community stochastic block models, the minimum vertex cover problem becomes hard when in-degree plus out-degree exceeds e, but becomes easy again when cross-community degree is large enough.
We now consider the process of picking up directed edge j→i at random from SBM at step t of WP
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Statistical mechanics of the minimum vertex cover problem in stochastic block models
For two-community stochastic block models, the minimum vertex cover problem becomes hard when in-degree plus out-degree exceeds e, but becomes easy again when cross-community degree is large enough.