Abstract:In this paper we study the connectivity properties of the random subgraph of the ncube generated by the k-out model and denoted by Q n (k). Let k be an integer, 1 ≤ k ≤ n−1. We let Q n (k) be the graph that is generated by independently including for every v ∈ V (Q n ) a set of k distinct edges chosen uniformly from all the n k sets of distinct edges that are incident to v. We study connectivity the properties of Q n (k) as k varies. We show that w.h.p. 1 Q n (1) does not contain a giant component i.e. a compo… Show more
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