## Planarity thresholds for two types of random subgraphs of the n-cube.(English)Zbl 0679.05062

Consider a random spanning (respectively induced) subgraph of the n-cube $$Q_ n$$ in which each edge (respectively vertex) is present with probability p, it is shown that $$2^{-n/14_ n-4/14}$$ (respectively $$2^{-n/11}n^{-4/11})$$ is the threshold probability for the planarity of this random graph.
Reviewer: G.Grimmett

### MSC:

 05C80 Random graphs (graph-theoretic aspects)

### Keywords:

random graph; planarity
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